第 25739 題：有限群第一同構定理

原題與已知條件

完整有限群、total homomorphism、kernel、image與quotient cosets的第一同構責任。操作=iso1-image-codomain-boundary；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]],"target_identity":0,"mapping":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整有限群、total homomorphism、kernel、image與quotient cosets的第一同構責任。操作=iso1-image-codomain-boundary；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]],"target_identity":0,"mapping":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

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。

• mko-first-isomorphism-theorem-finite-groups

逐步推導

source roles = [iso1-image-codomain-boundary]

derived = [[image, codomain_order, image_order, surjective_to_codomain, image_isomorphism_statement, codomain_scope, general_theorem_proof_claim, boundary]]

source roles = [Iso1 ORIGINAL SOURCE, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]], 0]

derived = [15, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14]], 是]

source roles = [Iso1 ORIGINAL SOURCE, 15, 0]

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 3375, [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]

source roles = [Iso1 ORIGINAL TARGET, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]], 0]

derived = [30, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14], [15, 15, 15, 15], [16, 16, 16, 16], [17, 17, 17, 17], [18, 18, 18, 18], [19, 19, 19, 19], [20, 20, 20, 20], [21, 21, 21, 21], [22, 22, 22, 22], [23, 23, 23, 23], [24, 24, 24, 24], [25, 25, 25, 25], [26, 26, 26, 26], [27, 27, 27, 27], [28, 28, 28, 28], [29, 29, 29, 29]], 是]

source roles = [Iso1 ORIGINAL TARGET, 30, 0]

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 27000, [0, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]

source roles = [Iso1 ACTUAL kernel, [0], 0]

derived = [是, [[0, 0, 0, 是]], 是, [[0, 0, 是]], 是, 是, [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是], [8, [0], 是], [9, [0], 是], [10, [0], 是], [11, [0], 是], [12, [0], 是], [13, [0], 是], [14, [0], 是]], 是]

source roles = [Iso1 ACTUAL image, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 0]

derived = [是, [[0, 0, 0, 是], [0, 2, 2, 是], [0, 4, 4, 是], [0, 6, 6, 是], [0, 8, 8, 是], [0, 10, 10, 是], [0, 12, 12, 是], [0, 14, 14, 是], [0, 16, 16, 是], [0, 18, 18, 是], [0, 20, 20, 是], [0, 22, 22, 是], [0, 24, 24, 是], [0, 26, 26, 是], [0, 28, 28, 是], [2, 0, 2, 是], [2, 2, 4, 是], [2, 4, 6, 是], [2, 6, 8, 是], [2, 8, 10, 是], [2, 10, 12, 是], [2, 12, 14, 是], [2, 14, 16, 是], [2, 16, 18, 是], [2, 18, 20, 是], [2, 20, 22, 是], [2, 22, 24, 是], [2, 24, 26, 是], [2, 26, 28, 是], [2, 28, 0, 是], [4, 0, 4, 是], [4, 2, 6, 是], [4, 4, 8, 是], [4, 6, 10, 是], [4, 8, 12, 是], [4, 10, 14, 是], [4, 12, 16, 是], [4, 14, 18, 是], [4, 16, 20, 是], [4, 18, 22, 是], [4, 20, 24, 是], [4, 22, 26, 是], [4, 24, 28, 是], [4, 26, 0, 是], [4, 28, 2, 是], [6, 0, 6, 是], [6, 2, 8, 是], [6, 4, 10, 是], [6, 6, 12, 是], [6, 8, 14, 是], [6, 10, 16, 是], [6, 12, 18, 是], [6, 14, 20, 是], [6, 16, 22, 是], [6, 18, 24, 是], [6, 20, 26, 是], [6, 22, 28, 是], [6, 24, 0, 是], [6, 26, 2, 是], [6, 28, 4, 是], [8, 0, 8, 是], [8, 2, 10, 是], [8, 4, 12, 是], [8, 6, 14, 是], [8, 8, 16, 是], [8, 10, 18, 是], [8, 12, 20, 是], [8, 14, 22, 是], [8, 16, 24, 是], [8, 18, 26, 是], [8, 20, 28, 是], [8, 22, 0, 是], [8, 24, 2, 是], [8, 26, 4, 是], [8, 28, 6, 是], [10, 0, 10, 是], [10, 2, 12, 是], [10, 4, 14, 是], [10, 6, 16, 是], [10, 8, 18, 是], [10, 10, 20, 是], [10, 12, 22, 是], [10, 14, 24, 是], [10, 16, 26, 是], [10, 18, 28, 是], [10, 20, 0, 是], [10, 22, 2, 是], [10, 24, 4, 是], [10, 26, 6, 是], [10, 28, 8, 是], [12, 0, 12, 是], [12, 2, 14, 是], [12, 4, 16, 是], [12, 6, 18, 是], [12, 8, 20, 是], [12, 10, 22, 是], [12, 12, 24, 是], [12, 14, 26, 是], [12, 16, 28, 是], [12, 18, 0, 是], [12, 20, 2, 是], [12, 22, 4, 是], [12, 24, 6, 是], [12, 26, 8, 是], [12, 28, 10, 是], [14, 0, 14, 是], [14, 2, 16, 是], [14, 4, 18, 是], [14, 6, 20, 是], [14, 8, 22, 是], [14, 10, 24, 是], [14, 12, 26, 是], [14, 14, 28, 是], [14, 16, 0, 是], [14, 18, 2, 是], [14, 20, 4, 是], [14, 22, 6, 是], [14, 24, 8, 是], [14, 26, 10, 是], [14, 28, 12, 是], [16, 0, 16, 是], [16, 2, 18, 是], [16, 4, 20, 是], [16, 6, 22, 是], [16, 8, 24, 是], [16, 10, 26, 是], [16, 12, 28, 是], [16, 14, 0, 是], [16, 16, 2, 是], [16, 18, 4, 是], [16, 20, 6, 是], [16, 22, 8, 是], [16, 24, 10, 是], [16, 26, 12, 是], [16, 28, 14, 是], [18, 0, 18, 是], [18, 2, 20, 是], [18, 4, 22, 是], [18, 6, 24, 是], [18, 8, 26, 是], [18, 10, 28, 是], [18, 12, 0, 是], [18, 14, 2, 是], [18, 16, 4, 是], [18, 18, 6, 是], [18, 20, 8, 是], [18, 22, 10, 是], [18, 24, 12, 是], [18, 26, 14, 是], [18, 28, 16, 是], [20, 0, 20, 是], [20, 2, 22, 是], [20, 4, 24, 是], [20, 6, 26, 是], [20, 8, 28, 是], [20, 10, 0, 是], [20, 12, 2, 是], [20, 14, 4, 是], [20, 16, 6, 是], [20, 18, 8, 是], [20, 20, 10, 是], [20, 22, 12, 是], [20, 24, 14, 是], [20, 26, 16, 是], [20, 28, 18, 是], [22, 0, 22, 是], [22, 2, 24, 是], [22, 4, 26, 是], [22, 6, 28, 是], [22, 8, 0, 是], [22, 10, 2, 是], [22, 12, 4, 是], [22, 14, 6, 是], [22, 16, 8, 是], [22, 18, 10, 是], [22, 20, 12, 是], [22, 22, 14, 是], [22, 24, 16, 是], [22, 26, 18, 是], [22, 28, 20, 是], [24, 0, 24, 是], [24, 2, 26, 是], [24, 4, 28, 是], [24, 6, 0, 是], [24, 8, 2, 是], [24, 10, 4, 是], [24, 12, 6, 是], [24, 14, 8, 是], [24, 16, 10, 是], [24, 18, 12, 是], [24, 20, 14, 是], [24, 22, 16, 是], [24, 24, 18, 是], [24, 26, 20, 是], [24, 28, 22, 是], [26, 0, 26, 是], [26, 2, 28, 是], [26, 4, 0, 是], [26, 6, 2, 是], [26, 8, 4, 是], [26, 10, 6, 是], [26, 12, 8, 是], [26, 14, 10, 是], [26, 16, 12, 是], [26, 18, 14, 是], [26, 20, 16, 是], [26, 22, 18, 是], [26, 24, 20, 是], [26, 26, 22, 是], [26, 28, 24, 是], [28, 0, 28, 是], [28, 2, 0, 是], [28, 4, 2, 是], [28, 6, 4, 是], [28, 8, 6, 是], [28, 10, 8, 是], [28, 12, 10, 是], [28, 14, 12, 是], [28, 16, 14, 是], [28, 18, 16, 是], [28, 20, 18, 是], [28, 22, 20, 是], [28, 24, 22, 是], [28, 26, 24, 是], [28, 28, 26, 是]], 是, [[0, 0, 是], [2, 28, 是], [4, 26, 是], [6, 24, 是], [8, 22, 是], [10, 20, 是], [12, 18, 是], [14, 16, 是], [16, 14, 是], [18, 12, 是], [20, 10, 是], [22, 8, 是], [24, 6, 是], [26, 4, 是], [28, 2, 是]], 是, 是, [[0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [2, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [3, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [4, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [5, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [6, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [7, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [8, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [9, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [10, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [11, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [12, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [13, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [14, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [15, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [16, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [17, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [18, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [19, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [20, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [21, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [22, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [23, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [24, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [25, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [26, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [27, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [28, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是], [29, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是]], 是]

source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 0, 0]

derived = [[[0, 0, 0, 0, 是], [0, 1, 2, 2, 是], [0, 2, 4, 4, 是], [0, 3, 6, 6, 是], [0, 4, 8, 8, 是], [0, 5, 10, 10, 是], [0, 6, 12, 12, 是], [0, 7, 14, 14, 是], [0, 8, 16, 16, 是], [0, 9, 18, 18, 是], [0, 10, 20, 20, 是], [0, 11, 22, 22, 是], [0, 12, 24, 24, 是], [0, 13, 26, 26, 是], [0, 14, 28, 28, 是], [1, 0, 2, 2, 是], [1, 1, 4, 4, 是], [1, 2, 6, 6, 是], [1, 3, 8, 8, 是], [1, 4, 10, 10, 是], [1, 5, 12, 12, 是], [1, 6, 14, 14, 是], [1, 7, 16, 16, 是], [1, 8, 18, 18, 是], [1, 9, 20, 20, 是], [1, 10, 22, 22, 是], [1, 11, 24, 24, 是], [1, 12, 26, 26, 是], [1, 13, 28, 28, 是], [1, 14, 0, 0, 是], [2, 0, 4, 4, 是], [2, 1, 6, 6, 是], [2, 2, 8, 8, 是], [2, 3, 10, 10, 是], [2, 4, 12, 12, 是], [2, 5, 14, 14, 是], [2, 6, 16, 16, 是], [2, 7, 18, 18, 是], [2, 8, 20, 20, 是], [2, 9, 22, 22, 是], [2, 10, 24, 24, 是], [2, 11, 26, 26, 是], [2, 12, 28, 28, 是], [2, 13, 0, 0, 是], [2, 14, 2, 2, 是], [3, 0, 6, 6, 是], [3, 1, 8, 8, 是], [3, 2, 10, 10, 是], [3, 3, 12, 12, 是], [3, 4, 14, 14, 是], [3, 5, 16, 16, 是], [3, 6, 18, 18, 是], [3, 7, 20, 20, 是], [3, 8, 22, 22, 是], [3, 9, 24, 24, 是], [3, 10, 26, 26, 是], [3, 11, 28, 28, 是], [3, 12, 0, 0, 是], [3, 13, 2, 2, 是], [3, 14, 4, 4, 是], [4, 0, 8, 8, 是], [4, 1, 10, 10, 是], [4, 2, 12, 12, 是], [4, 3, 14, 14, 是], [4, 4, 16, 16, 是], [4, 5, 18, 18, 是], [4, 6, 20, 20, 是], [4, 7, 22, 22, 是], [4, 8, 24, 24, 是], [4, 9, 26, 26, 是], [4, 10, 28, 28, 是], [4, 11, 0, 0, 是], [4, 12, 2, 2, 是], [4, 13, 4, 4, 是], [4, 14, 6, 6, 是], [5, 0, 10, 10, 是], [5, 1, 12, 12, 是], [5, 2, 14, 14, 是], [5, 3, 16, 16, 是], [5, 4, 18, 18, 是], [5, 5, 20, 20, 是], [5, 6, 22, 22, 是], [5, 7, 24, 24, 是], [5, 8, 26, 26, 是], [5, 9, 28, 28, 是], [5, 10, 0, 0, 是], [5, 11, 2, 2, 是], [5, 12, 4, 4, 是], [5, 13, 6, 6, 是], [5, 14, 8, 8, 是], [6, 0, 12, 12, 是], [6, 1, 14, 14, 是], [6, 2, 16, 16, 是], [6, 3, 18, 18, 是], [6, 4, 20, 20, 是], [6, 5, 22, 22, 是], [6, 6, 24, 24, 是], [6, 7, 26, 26, 是], [6, 8, 28, 28, 是], [6, 9, 0, 0, 是], [6, 10, 2, 2, 是], [6, 11, 4, 4, 是], [6, 12, 6, 6, 是], [6, 13, 8, 8, 是], [6, 14, 10, 10, 是], [7, 0, 14, 14, 是], [7, 1, 16, 16, 是], [7, 2, 18, 18, 是], [7, 3, 20, 20, 是], [7, 4, 22, 22, 是], [7, 5, 24, 24, 是], [7, 6, 26, 26, 是], [7, 7, 28, 28, 是], [7, 8, 0, 0, 是], [7, 9, 2, 2, 是], [7, 10, 4, 4, 是], [7, 11, 6, 6, 是], [7, 12, 8, 8, 是], [7, 13, 10, 10, 是], [7, 14, 12, 12, 是], [8, 0, 16, 16, 是], [8, 1, 18, 18, 是], [8, 2, 20, 20, 是], [8, 3, 22, 22, 是], [8, 4, 24, 24, 是], [8, 5, 26, 26, 是], [8, 6, 28, 28, 是], [8, 7, 0, 0, 是], [8, 8, 2, 2, 是], [8, 9, 4, 4, 是], [8, 10, 6, 6, 是], [8, 11, 8, 8, 是], [8, 12, 10, 10, 是], [8, 13, 12, 12, 是], [8, 14, 14, 14, 是], [9, 0, 18, 18, 是], [9, 1, 20, 20, 是], [9, 2, 22, 22, 是], [9, 3, 24, 24, 是], [9, 4, 26, 26, 是], [9, 5, 28, 28, 是], [9, 6, 0, 0, 是], [9, 7, 2, 2, 是], [9, 8, 4, 4, 是], [9, 9, 6, 6, 是], [9, 10, 8, 8, 是], [9, 11, 10, 10, 是], [9, 12, 12, 12, 是], [9, 13, 14, 14, 是], [9, 14, 16, 16, 是], [10, 0, 20, 20, 是], [10, 1, 22, 22, 是], [10, 2, 24, 24, 是], [10, 3, 26, 26, 是], [10, 4, 28, 28, 是], [10, 5, 0, 0, 是], [10, 6, 2, 2, 是], [10, 7, 4, 4, 是], [10, 8, 6, 6, 是], [10, 9, 8, 8, 是], [10, 10, 10, 10, 是], [10, 11, 12, 12, 是], [10, 12, 14, 14, 是], [10, 13, 16, 16, 是], [10, 14, 18, 18, 是], [11, 0, 22, 22, 是], [11, 1, 24, 24, 是], [11, 2, 26, 26, 是], [11, 3, 28, 28, 是], [11, 4, 0, 0, 是], [11, 5, 2, 2, 是], [11, 6, 4, 4, 是], [11, 7, 6, 6, 是], [11, 8, 8, 8, 是], [11, 9, 10, 10, 是], [11, 10, 12, 12, 是], [11, 11, 14, 14, 是], [11, 12, 16, 16, 是], [11, 13, 18, 18, 是], [11, 14, 20, 20, 是], [12, 0, 24, 24, 是], [12, 1, 26, 26, 是], [12, 2, 28, 28, 是], [12, 3, 0, 0, 是], [12, 4, 2, 2, 是], [12, 5, 4, 4, 是], [12, 6, 6, 6, 是], [12, 7, 8, 8, 是], [12, 8, 10, 10, 是], [12, 9, 12, 12, 是], [12, 10, 14, 14, 是], [12, 11, 16, 16, 是], [12, 12, 18, 18, 是], [12, 13, 20, 20, 是], [12, 14, 22, 22, 是], [13, 0, 26, 26, 是], [13, 1, 28, 28, 是], [13, 2, 0, 0, 是], [13, 3, 2, 2, 是], [13, 4, 4, 4, 是], [13, 5, 6, 6, 是], [13, 6, 8, 8, 是], [13, 7, 10, 10, 是], [13, 8, 12, 12, 是], [13, 9, 14, 14, 是], [13, 10, 16, 16, 是], [13, 11, 18, 18, 是], [13, 12, 20, 20, 是], [13, 13, 22, 22, 是], [13, 14, 24, 24, 是], [14, 0, 28, 28, 是], [14, 1, 0, 0, 是], [14, 2, 2, 2, 是], [14, 3, 4, 4, 是], [14, 4, 6, 6, 是], [14, 5, 8, 8, 是], [14, 6, 10, 10, 是], [14, 7, 12, 12, 是], [14, 8, 14, 14, 是], [14, 9, 16, 16, 是], [14, 10, 18, 18, 是], [14, 11, 20, 20, 是], [14, 12, 22, 22, 是], [14, 13, 24, 24, 是], [14, 14, 26, 26, 是]], 是, null, [0], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 是, 是]

source roles = [[0], 是, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28]]

derived = [[[0], [1], [10], [11], [12], [13], [14], [2], [3], [4], [5], [6], [7], [8], [9]], [0, 1, 7, 8, 9, 10, 11, 12, 13, 14, 2, 3, 4, 5, 6], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [1, 7, 3, 4, 5, 6, 0, 8, 9, 10, 11, 12, 13, 14, 2], [2, 3, 10, 11, 12, 13, 14, 4, 5, 6, 0, 1, 7, 8, 9], [3, 4, 11, 12, 13, 14, 2, 5, 6, 0, 1, 7, 8, 9, 10], [4, 5, 12, 13, 14, 2, 3, 6, 0, 1, 7, 8, 9, 10, 11], [5, 6, 13, 14, 2, 3, 4, 0, 1, 7, 8, 9, 10, 11, 12], [6, 0, 14, 2, 3, 4, 5, 1, 7, 8, 9, 10, 11, 12, 13], [7, 8, 4, 5, 6, 0, 1, 9, 10, 11, 12, 13, 14, 2, 3], [8, 9, 5, 6, 0, 1, 7, 10, 11, 12, 13, 14, 2, 3, 4], [9, 10, 6, 0, 1, 7, 8, 11, 12, 13, 14, 2, 3, 4, 5], [10, 11, 0, 1, 7, 8, 9, 12, 13, 14, 2, 3, 4, 5, 6], [11, 12, 1, 7, 8, 9, 10, 13, 14, 2, 3, 4, 5, 6, 0], [12, 13, 7, 8, 9, 10, 11, 14, 2, 3, 4, 5, 6, 0, 1], [13, 14, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 0, 1, 7], [14, 2, 9, 10, 11, 12, 13, 3, 4, 5, 6, 0, 1, 7, 8]], [[0, 0, [0], 是], [0, 1, [1], 是], [0, 2, [2], 是], [0, 3, [3], 是], [0, 4, [4], 是], [0, 5, [5], 是], [0, 6, [6], 是], [0, 7, [7], 是], [0, 8, [8], 是], [0, 9, [9], 是], [0, 10, [10], 是], [0, 11, [11], 是], [0, 12, [12], 是], [0, 13, [13], 是], [0, 14, [14], 是], [1, 0, [1], 是], [1, 1, [7], 是], [1, 2, [3], 是], [1, 3, [4], 是], [1, 4, [5], 是], [1, 5, [6], 是], [1, 6, [0], 是], [1, 7, [8], 是], [1, 8, [9], 是], [1, 9, [10], 是], [1, 10, [11], 是], [1, 11, [12], 是], [1, 12, [13], 是], [1, 13, [14], 是], [1, 14, [2], 是], [2, 0, [2], 是], [2, 1, [3], 是], [2, 2, [10], 是], [2, 3, [11], 是], [2, 4, [12], 是], [2, 5, [13], 是], [2, 6, [14], 是], [2, 7, [4], 是], [2, 8, [5], 是], [2, 9, [6], 是], [2, 10, [0], 是], [2, 11, [1], 是], [2, 12, [7], 是], [2, 13, [8], 是], [2, 14, [9], 是], [3, 0, [3], 是], [3, 1, [4], 是], [3, 2, [11], 是], [3, 3, [12], 是], [3, 4, [13], 是], [3, 5, [14], 是], [3, 6, [2], 是], [3, 7, [5], 是], [3, 8, [6], 是], [3, 9, [0], 是], [3, 10, [1], 是], [3, 11, [7], 是], [3, 12, [8], 是], [3, 13, [9], 是], [3, 14, [10], 是], [4, 0, [4], 是], [4, 1, [5], 是], [4, 2, [12], 是], [4, 3, [13], 是], [4, 4, [14], 是], [4, 5, [2], 是], [4, 6, [3], 是], [4, 7, [6], 是], [4, 8, [0], 是], [4, 9, [1], 是], [4, 10, [7], 是], [4, 11, [8], 是], [4, 12, [9], 是], [4, 13, [10], 是], [4, 14, [11], 是], [5, 0, [5], 是], [5, 1, [6], 是], [5, 2, [13], 是], [5, 3, [14], 是], [5, 4, [2], 是], [5, 5, [3], 是], [5, 6, [4], 是], [5, 7, [0], 是], [5, 8, [1], 是], [5, 9, [7], 是], [5, 10, [8], 是], [5, 11, [9], 是], [5, 12, [10], 是], [5, 13, [11], 是], [5, 14, [12], 是], [6, 0, [6], 是], [6, 1, [0], 是], [6, 2, [14], 是], [6, 3, [2], 是], [6, 4, [3], 是], [6, 5, [4], 是], [6, 6, [5], 是], [6, 7, [1], 是], [6, 8, [7], 是], [6, 9, [8], 是], [6, 10, [9], 是], [6, 11, [10], 是], [6, 12, [11], 是], [6, 13, [12], 是], [6, 14, [13], 是], [7, 0, [7], 是], [7, 1, [8], 是], [7, 2, [4], 是], [7, 3, [5], 是], [7, 4, [6], 是], [7, 5, [0], 是], [7, 6, [1], 是], [7, 7, [9], 是], [7, 8, [10], 是], [7, 9, [11], 是], [7, 10, [12], 是], [7, 11, [13], 是], [7, 12, [14], 是], [7, 13, [2], 是], [7, 14, [3], 是], [8, 0, [8], 是], [8, 1, [9], 是], [8, 2, [5], 是], [8, 3, [6], 是], [8, 4, [0], 是], [8, 5, [1], 是], [8, 6, [7], 是], [8, 7, [10], 是], [8, 8, [11], 是], [8, 9, [12], 是], [8, 10, [13], 是], [8, 11, [14], 是], [8, 12, [2], 是], [8, 13, [3], 是], [8, 14, [4], 是], [9, 0, [9], 是], [9, 1, [10], 是], [9, 2, [6], 是], [9, 3, [0], 是], [9, 4, [1], 是], [9, 5, [7], 是], [9, 6, [8], 是], [9, 7, [11], 是], [9, 8, [12], 是], [9, 9, [13], 是], [9, 10, [14], 是], [9, 11, [2], 是], [9, 12, [3], 是], [9, 13, [4], 是], [9, 14, [5], 是], [10, 0, [10], 是], [10, 1, [11], 是], [10, 2, [0], 是], [10, 3, [1], 是], [10, 4, [7], 是], [10, 5, [8], 是], [10, 6, [9], 是], [10, 7, [12], 是], [10, 8, [13], 是], [10, 9, [14], 是], [10, 10, [2], 是], [10, 11, [3], 是], [10, 12, [4], 是], [10, 13, [5], 是], [10, 14, [6], 是], [11, 0, [11], 是], [11, 1, [12], 是], [11, 2, [1], 是], [11, 3, [7], 是], [11, 4, [8], 是], [11, 5, [9], 是], [11, 6, [10], 是], [11, 7, [13], 是], [11, 8, [14], 是], [11, 9, [2], 是], [11, 10, [3], 是], [11, 11, [4], 是], [11, 12, [5], 是], [11, 13, [6], 是], [11, 14, [0], 是], [12, 0, [12], 是], [12, 1, [13], 是], [12, 2, [7], 是], [12, 3, [8], 是], [12, 4, [9], 是], [12, 5, [10], 是], [12, 6, [11], 是], [12, 7, [14], 是], [12, 8, [2], 是], [12, 9, [3], 是], [12, 10, [4], 是], [12, 11, [5], 是], [12, 12, [6], 是], [12, 13, [0], 是], [12, 14, [1], 是], [13, 0, [13], 是], [13, 1, [14], 是], [13, 2, [8], 是], [13, 3, [9], 是], [13, 4, [10], 是], [13, 5, [11], 是], [13, 6, [12], 是], [13, 7, [2], 是], [13, 8, [3], 是], [13, 9, [4], 是], [13, 10, [5], 是], [13, 11, [6], 是], [13, 12, [0], 是], [13, 13, [1], 是], [13, 14, [7], 是], [14, 0, [14], 是], [14, 1, [2], 是], [14, 2, [9], 是], [14, 3, [10], 是], [14, 4, [11], 是], [14, 5, [12], 是], [14, 6, [13], 是], [14, 7, [3], 是], [14, 8, [4], 是], [14, 9, [5], 是], [14, 10, [6], 是], [14, 11, [0], 是], [14, 12, [1], 是], [14, 13, [7], 是], [14, 14, [8], 是]], [[0, [0], [0], 是], [1, [1], [2], 是], [2, [10], [20], 是], [3, [11], [22], 是], [4, [12], [24], 是], [5, [13], [26], 是], [6, [14], [28], 是], [7, [2], [4], 是], [8, [3], [6], 是], [9, [4], [8], 是], [10, [5], [10], 是], [11, [6], [12], 是], [12, [7], [14], 是], [13, [8], [16], 是], [14, [9], [18], 是]], 是]

source roles = [[[0], [1], [10], [11], [12], [13], [14], [2], [3], [4], [5], [6], [7], [8], [9]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], [0, 2, 20, 22, 24, 26, 28, 4, 6, 8, 10, 12, 14, 16, 18]]

derived = [[[0, 0, 0, 0, 是], [0, 1, 2, 2, 是], [0, 2, 20, 20, 是], [0, 3, 22, 22, 是], [0, 4, 24, 24, 是], [0, 5, 26, 26, 是], [0, 6, 28, 28, 是], [0, 7, 4, 4, 是], [0, 8, 6, 6, 是], [0, 9, 8, 8, 是], [0, 10, 10, 10, 是], [0, 11, 12, 12, 是], [0, 12, 14, 14, 是], [0, 13, 16, 16, 是], [0, 14, 18, 18, 是], [1, 0, 2, 2, 是], [1, 1, 4, 4, 是], [1, 2, 22, 22, 是], [1, 3, 24, 24, 是], [1, 4, 26, 26, 是], [1, 5, 28, 28, 是], [1, 6, 0, 0, 是], [1, 7, 6, 6, 是], [1, 8, 8, 8, 是], [1, 9, 10, 10, 是], [1, 10, 12, 12, 是], [1, 11, 14, 14, 是], [1, 12, 16, 16, 是], [1, 13, 18, 18, 是], [1, 14, 20, 20, 是], [2, 0, 20, 20, 是], [2, 1, 22, 22, 是], [2, 2, 10, 10, 是], [2, 3, 12, 12, 是], [2, 4, 14, 14, 是], [2, 5, 16, 16, 是], [2, 6, 18, 18, 是], [2, 7, 24, 24, 是], [2, 8, 26, 26, 是], [2, 9, 28, 28, 是], [2, 10, 0, 0, 是], [2, 11, 2, 2, 是], [2, 12, 4, 4, 是], [2, 13, 6, 6, 是], [2, 14, 8, 8, 是], [3, 0, 22, 22, 是], [3, 1, 24, 24, 是], [3, 2, 12, 12, 是], [3, 3, 14, 14, 是], [3, 4, 16, 16, 是], [3, 5, 18, 18, 是], [3, 6, 20, 20, 是], [3, 7, 26, 26, 是], [3, 8, 28, 28, 是], [3, 9, 0, 0, 是], [3, 10, 2, 2, 是], [3, 11, 4, 4, 是], [3, 12, 6, 6, 是], [3, 13, 8, 8, 是], [3, 14, 10, 10, 是], [4, 0, 24, 24, 是], [4, 1, 26, 26, 是], [4, 2, 14, 14, 是], [4, 3, 16, 16, 是], [4, 4, 18, 18, 是], [4, 5, 20, 20, 是], [4, 6, 22, 22, 是], [4, 7, 28, 28, 是], [4, 8, 0, 0, 是], [4, 9, 2, 2, 是], [4, 10, 4, 4, 是], [4, 11, 6, 6, 是], [4, 12, 8, 8, 是], [4, 13, 10, 10, 是], [4, 14, 12, 12, 是], [5, 0, 26, 26, 是], [5, 1, 28, 28, 是], [5, 2, 16, 16, 是], [5, 3, 18, 18, 是], [5, 4, 20, 20, 是], [5, 5, 22, 22, 是], [5, 6, 24, 24, 是], [5, 7, 0, 0, 是], [5, 8, 2, 2, 是], [5, 9, 4, 4, 是], [5, 10, 6, 6, 是], [5, 11, 8, 8, 是], [5, 12, 10, 10, 是], [5, 13, 12, 12, 是], [5, 14, 14, 14, 是], [6, 0, 28, 28, 是], [6, 1, 0, 0, 是], [6, 2, 18, 18, 是], [6, 3, 20, 20, 是], [6, 4, 22, 22, 是], [6, 5, 24, 24, 是], [6, 6, 26, 26, 是], [6, 7, 2, 2, 是], [6, 8, 4, 4, 是], [6, 9, 6, 6, 是], [6, 10, 8, 8, 是], [6, 11, 10, 10, 是], [6, 12, 12, 12, 是], [6, 13, 14, 14, 是], [6, 14, 16, 16, 是], [7, 0, 4, 4, 是], [7, 1, 6, 6, 是], [7, 2, 24, 24, 是], [7, 3, 26, 26, 是], [7, 4, 28, 28, 是], [7, 5, 0, 0, 是], [7, 6, 2, 2, 是], [7, 7, 8, 8, 是], [7, 8, 10, 10, 是], [7, 9, 12, 12, 是], [7, 10, 14, 14, 是], [7, 11, 16, 16, 是], [7, 12, 18, 18, 是], [7, 13, 20, 20, 是], [7, 14, 22, 22, 是], [8, 0, 6, 6, 是], [8, 1, 8, 8, 是], [8, 2, 26, 26, 是], [8, 3, 28, 28, 是], [8, 4, 0, 0, 是], [8, 5, 2, 2, 是], [8, 6, 4, 4, 是], [8, 7, 10, 10, 是], [8, 8, 12, 12, 是], [8, 9, 14, 14, 是], [8, 10, 16, 16, 是], [8, 11, 18, 18, 是], [8, 12, 20, 20, 是], [8, 13, 22, 22, 是], [8, 14, 24, 24, 是], [9, 0, 8, 8, 是], [9, 1, 10, 10, 是], [9, 2, 28, 28, 是], [9, 3, 0, 0, 是], [9, 4, 2, 2, 是], [9, 5, 4, 4, 是], [9, 6, 6, 6, 是], [9, 7, 12, 12, 是], [9, 8, 14, 14, 是], [9, 9, 16, 16, 是], [9, 10, 18, 18, 是], [9, 11, 20, 20, 是], [9, 12, 22, 22, 是], [9, 13, 24, 24, 是], [9, 14, 26, 26, 是], [10, 0, 10, 10, 是], [10, 1, 12, 12, 是], [10, 2, 0, 0, 是], [10, 3, 2, 2, 是], [10, 4, 4, 4, 是], [10, 5, 6, 6, 是], [10, 6, 8, 8, 是], [10, 7, 14, 14, 是], [10, 8, 16, 16, 是], [10, 9, 18, 18, 是], [10, 10, 20, 20, 是], [10, 11, 22, 22, 是], [10, 12, 24, 24, 是], [10, 13, 26, 26, 是], [10, 14, 28, 28, 是], [11, 0, 12, 12, 是], [11, 1, 14, 14, 是], [11, 2, 2, 2, 是], [11, 3, 4, 4, 是], [11, 4, 6, 6, 是], [11, 5, 8, 8, 是], [11, 6, 10, 10, 是], [11, 7, 16, 16, 是], [11, 8, 18, 18, 是], [11, 9, 20, 20, 是], [11, 10, 22, 22, 是], [11, 11, 24, 24, 是], [11, 12, 26, 26, 是], [11, 13, 28, 28, 是], [11, 14, 0, 0, 是], [12, 0, 14, 14, 是], [12, 1, 16, 16, 是], [12, 2, 4, 4, 是], [12, 3, 6, 6, 是], [12, 4, 8, 8, 是], [12, 5, 10, 10, 是], [12, 6, 12, 12, 是], [12, 7, 18, 18, 是], [12, 8, 20, 20, 是], [12, 9, 22, 22, 是], [12, 10, 24, 24, 是], [12, 11, 26, 26, 是], [12, 12, 28, 28, 是], [12, 13, 0, 0, 是], [12, 14, 2, 2, 是], [13, 0, 16, 16, 是], [13, 1, 18, 18, 是], [13, 2, 6, 6, 是], [13, 3, 8, 8, 是], [13, 4, 10, 10, 是], [13, 5, 12, 12, 是], [13, 6, 14, 14, 是], [13, 7, 20, 20, 是], [13, 8, 22, 22, 是], [13, 9, 24, 24, 是], [13, 10, 26, 26, 是], [13, 11, 28, 28, 是], [13, 12, 0, 0, 是], [13, 13, 2, 2, 是], [13, 14, 4, 4, 是], [14, 0, 18, 18, 是], [14, 1, 20, 20, 是], [14, 2, 8, 8, 是], [14, 3, 10, 10, 是], [14, 4, 12, 12, 是], [14, 5, 14, 14, 是], [14, 6, 16, 16, 是], [14, 7, 22, 22, 是], [14, 8, 24, 24, 是], [14, 9, 26, 26, 是], [14, 10, 28, 28, 是], [14, 11, 0, 0, 是], [14, 12, 2, 2, 是], [14, 13, 4, 4, 是], [14, 14, 6, 6, 是]], 是, 是, 是, 是, 否]

source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 30, 15]

derived = [否, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, 否]

逐步反向核對

• S011 · 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。
• S010 · 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。
• S009 · 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。
• S008 · 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。
• S007 · 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。
• S006 · 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。
• 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。

結論

([0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28], 30, 15, 否, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, 否, finite_instance_certificate_not_a_general_theorem_proof)

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。

本題覆核與來源綁定

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。