# 第 25374 題：有限商群 [返回所在分頁 127](https://ocme.evemisslab.com/zh-Hant/questions/page/127/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261015-advance-20261114-r02-finite-quotient-group-foundations/#q-20261015-advance-20261114-r02-finite-quotient-group-0024) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0049-25374 · q-20261015-advance-20261114-r02-finite-quotient-group-0024 ## 原題與已知條件 完整有限群、subgroup與全部coset partition及代表元責任。操作=quotient-normal-coset-partition；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]],"identity":0,"subset":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — 完整有限群、subgroup與全部coset partition及代表元責任。操作=quotient-normal-coset-partition；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[36,37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[37,38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[38,39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[39,40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[40,41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[41,42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[42,43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[43,44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[44,45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[45,46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[46,47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[47,48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[48,49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[49,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]],"identity":0,"subset":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48]}。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-finite-quotient-group](https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-quotient-group/) ## 逐步推導 S001 · implies操作前 source roles = [quotient-normal-coset-partition] 操作後 derived = [[subgroup, normal, cosets, partition_certificate, coset_count, certificate]] 條件：無 本頁列完整來源欄序，不需JavaScript；LP三種mode雖同為6欄，角色仍由原mode選，不由答案形狀猜。 步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001 S002 · implies操作前 source roles = [[[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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30], [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33], [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34], [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36], [38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37], [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [42, 43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [43, 44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [44, 45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [45, 46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [46, 47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [47, 48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], [48, 49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [49, 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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48]], 0] 操作後 derived = [50, [[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], [30, 30, 30, 30], [31, 31, 31, 31], [32, 32, 32, 32], [33, 33, 33, 33], [34, 34, 34, 34], [35, 35, 35, 35], [36, 36, 36, 36], [37, 37, 37, 37], [38, 38, 38, 38], [39, 39, 39, 39], [40, 40, 40, 40], [41, 41, 41, 41], [42, 42, 42, 42], [43, 43, 43, 43], [44, 44, 44, 44], [45, 45, 45, 45], [46, 46, 46, 46], [47, 47, 47, 47], [48, 48, 48, 48], [49, 49, 49, 49]], 是] 條件：無 先核整個closed Cayley table與實際identity標籤，不假設0或套舊上限32。 步驟識別與依賴規則：Quotient_complete_group_table_actual_identity · 依賴：G001, S001 S003 · implies操作前 source roles = [50, 0] 操作後 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, 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11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]] 條件：無 每個(x,y)矩陣格核全部z的(xy)z=x(yz)，共n³責任；每個inverse同時左右乘回同一identity。完整查核不靠抽樣。 步驟識別與依賴規則：Quotient_ALL_group_associativity_triples_and_two_sided_inverses · 依賴：G001, S002 S004 · implies操作前 source roles = [0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]] 操作後 derived = [[[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], [0, 30, 30, 是], [0, 32, 32, 是], [0, 34, 34, 是], [0, 36, 36, 是], [0, 38, 38, 是], [0, 40, 40, 是], [0, 42, 42, 是], [0, 44, 44, 是], [0, 46, 46, 是], [0, 48, 48, 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, 30, 是], [2, 30, 32, 是], [2, 32, 34, 是], [2, 34, 36, 是], [2, 36, 38, 是], [2, 38, 40, 是], [2, 40, 42, 是], [2, 42, 44, 是], [2, 44, 46, 是], [2, 46, 48, 是], [2, 48, 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, 30, 是], [4, 28, 32, 是], [4, 30, 34, 是], [4, 32, 36, 是], [4, 34, 38, 是], [4, 36, 40, 是], [4, 38, 42, 是], [4, 40, 44, 是], [4, 42, 46, 是], [4, 44, 48, 是], [4, 46, 0, 是], [4, 48, 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, 30, 是], [6, 26, 32, 是], [6, 28, 34, 是], [6, 30, 36, 是], [6, 32, 38, 是], [6, 34, 40, 是], [6, 36, 42, 是], [6, 38, 44, 是], [6, 40, 46, 是], [6, 42, 48, 是], [6, 44, 0, 是], [6, 46, 2, 是], [6, 48, 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, 30, 是], [8, 24, 32, 是], [8, 26, 34, 是], [8, 28, 36, 是], [8, 30, 38, 是], [8, 32, 40, 是], [8, 34, 42, 是], [8, 36, 44, 是], [8, 38, 46, 是], [8, 40, 48, 是], [8, 42, 0, 是], [8, 44, 2, 是], [8, 46, 4, 是], [8, 48, 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, 30, 是], [10, 22, 32, 是], [10, 24, 34, 是], [10, 26, 36, 是], [10, 28, 38, 是], [10, 30, 40, 是], [10, 32, 42, 是], [10, 34, 44, 是], [10, 36, 46, 是], [10, 38, 48, 是], [10, 40, 0, 是], [10, 42, 2, 是], [10, 44, 4, 是], [10, 46, 6, 是], [10, 48, 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, 30, 是], [12, 20, 32, 是], [12, 22, 34, 是], [12, 24, 36, 是], [12, 26, 38, 是], [12, 28, 40, 是], [12, 30, 42, 是], [12, 32, 44, 是], [12, 34, 46, 是], [12, 36, 48, 是], [12, 38, 0, 是], [12, 40, 2, 是], [12, 42, 4, 是], [12, 44, 6, 是], [12, 46, 8, 是], [12, 48, 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, 30, 是], [14, 18, 32, 是], [14, 20, 34, 是], [14, 22, 36, 是], [14, 24, 38, 是], [14, 26, 40, 是], [14, 28, 42, 是], [14, 30, 44, 是], [14, 32, 46, 是], [14, 34, 48, 是], [14, 36, 0, 是], [14, 38, 2, 是], [14, 40, 4, 是], [14, 42, 6, 是], [14, 44, 8, 是], [14, 46, 10, 是], [14, 48, 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, 30, 是], [16, 16, 32, 是], [16, 18, 34, 是], [16, 20, 36, 是], [16, 22, 38, 是], [16, 24, 40, 是], [16, 26, 42, 是], [16, 28, 44, 是], [16, 30, 46, 是], [16, 32, 48, 是], [16, 34, 0, 是], [16, 36, 2, 是], [16, 38, 4, 是], [16, 40, 6, 是], [16, 42, 8, 是], [16, 44, 10, 是], [16, 46, 12, 是], [16, 48, 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, 30, 是], [18, 14, 32, 是], [18, 16, 34, 是], [18, 18, 36, 是], [18, 20, 38, 是], [18, 22, 40, 是], [18, 24, 42, 是], [18, 26, 44, 是], [18, 28, 46, 是], [18, 30, 48, 是], [18, 32, 0, 是], [18, 34, 2, 是], [18, 36, 4, 是], [18, 38, 6, 是], [18, 40, 8, 是], [18, 42, 10, 是], [18, 44, 12, 是], [18, 46, 14, 是], [18, 48, 16, 是], [20, 0, 20, 是], [20, 2, 22, 是], [20, 4, 24, 是], [20, 6, 26, 是], [20, 8, 28, 是], [20, 10, 30, 是], [20, 12, 32, 是], [20, 14, 34, 是], [20, 16, 36, 是], [20, 18, 38, 是], [20, 20, 40, 是], [20, 22, 42, 是], [20, 24, 44, 是], [20, 26, 46, 是], [20, 28, 48, 是], [20, 30, 0, 是], [20, 32, 2, 是], [20, 34, 4, 是], [20, 36, 6, 是], [20, 38, 8, 是], [20, 40, 10, 是], [20, 42, 12, 是], [20, 44, 14, 是], [20, 46, 16, 是], [20, 48, 18, 是], [22, 0, 22, 是], [22, 2, 24, 是], [22, 4, 26, 是], [22, 6, 28, 是], [22, 8, 30, 是], [22, 10, 32, 是], [22, 12, 34, 是], [22, 14, 36, 是], [22, 16, 38, 是], [22, 18, 40, 是], [22, 20, 42, 是], [22, 22, 44, 是], [22, 24, 46, 是], [22, 26, 48, 是], [22, 28, 0, 是], [22, 30, 2, 是], [22, 32, 4, 是], [22, 34, 6, 是], [22, 36, 8, 是], [22, 38, 10, 是], [22, 40, 12, 是], [22, 42, 14, 是], [22, 44, 16, 是], [22, 46, 18, 是], [22, 48, 20, 是], [24, 0, 24, 是], [24, 2, 26, 是], [24, 4, 28, 是], [24, 6, 30, 是], [24, 8, 32, 是], [24, 10, 34, 是], [24, 12, 36, 是], [24, 14, 38, 是], [24, 16, 40, 是], [24, 18, 42, 是], [24, 20, 44, 是], [24, 22, 46, 是], [24, 24, 48, 是], [24, 26, 0, 是], [24, 28, 2, 是], [24, 30, 4, 是], [24, 32, 6, 是], [24, 34, 8, 是], [24, 36, 10, 是], [24, 38, 12, 是], [24, 40, 14, 是], [24, 42, 16, 是], [24, 44, 18, 是], [24, 46, 20, 是], [24, 48, 22, 是], [26, 0, 26, 是], [26, 2, 28, 是], [26, 4, 30, 是], [26, 6, 32, 是], [26, 8, 34, 是], [26, 10, 36, 是], [26, 12, 38, 是], [26, 14, 40, 是], [26, 16, 42, 是], [26, 18, 44, 是], [26, 20, 46, 是], [26, 22, 48, 是], [26, 24, 0, 是], [26, 26, 2, 是], [26, 28, 4, 是], [26, 30, 6, 是], [26, 32, 8, 是], [26, 34, 10, 是], [26, 36, 12, 是], [26, 38, 14, 是], [26, 40, 16, 是], [26, 42, 18, 是], [26, 44, 20, 是], [26, 46, 22, 是], [26, 48, 24, 是], [28, 0, 28, 是], [28, 2, 30, 是], [28, 4, 32, 是], [28, 6, 34, 是], [28, 8, 36, 是], [28, 10, 38, 是], [28, 12, 40, 是], [28, 14, 42, 是], [28, 16, 44, 是], [28, 18, 46, 是], [28, 20, 48, 是], [28, 22, 0, 是], [28, 24, 2, 是], [28, 26, 4, 是], [28, 28, 6, 是], [28, 30, 8, 是], [28, 32, 10, 是], [28, 34, 12, 是], [28, 36, 14, 是], [28, 38, 16, 是], [28, 40, 18, 是], [28, 42, 20, 是], [28, 44, 22, 是], [28, 46, 24, 是], [28, 48, 26, 是], [30, 0, 30, 是], [30, 2, 32, 是], [30, 4, 34, 是], [30, 6, 36, 是], [30, 8, 38, 是], [30, 10, 40, 是], [30, 12, 42, 是], [30, 14, 44, 是], [30, 16, 46, 是], [30, 18, 48, 是], [30, 20, 0, 是], [30, 22, 2, 是], [30, 24, 4, 是], [30, 26, 6, 是], [30, 28, 8, 是], [30, 30, 10, 是], [30, 32, 12, 是], [30, 34, 14, 是], [30, 36, 16, 是], [30, 38, 18, 是], [30, 40, 20, 是], [30, 42, 22, 是], [30, 44, 24, 是], [30, 46, 26, 是], [30, 48, 28, 是], [32, 0, 32, 是], [32, 2, 34, 是], [32, 4, 36, 是], [32, 6, 38, 是], [32, 8, 40, 是], [32, 10, 42, 是], [32, 12, 44, 是], [32, 14, 46, 是], [32, 16, 48, 是], [32, 18, 0, 是], [32, 20, 2, 是], [32, 22, 4, 是], [32, 24, 6, 是], [32, 26, 8, 是], [32, 28, 10, 是], [32, 30, 12, 是], [32, 32, 14, 是], [32, 34, 16, 是], [32, 36, 18, 是], [32, 38, 20, 是], [32, 40, 22, 是], [32, 42, 24, 是], [32, 44, 26, 是], [32, 46, 28, 是], [32, 48, 30, 是], [34, 0, 34, 是], [34, 2, 36, 是], [34, 4, 38, 是], [34, 6, 40, 是], [34, 8, 42, 是], [34, 10, 44, 是], [34, 12, 46, 是], [34, 14, 48, 是], [34, 16, 0, 是], [34, 18, 2, 是], [34, 20, 4, 是], [34, 22, 6, 是], [34, 24, 8, 是], [34, 26, 10, 是], [34, 28, 12, 是], [34, 30, 14, 是], [34, 32, 16, 是], [34, 34, 18, 是], [34, 36, 20, 是], [34, 38, 22, 是], [34, 40, 24, 是], [34, 42, 26, 是], [34, 44, 28, 是], [34, 46, 30, 是], [34, 48, 32, 是], [36, 0, 36, 是], [36, 2, 38, 是], [36, 4, 40, 是], [36, 6, 42, 是], [36, 8, 44, 是], [36, 10, 46, 是], [36, 12, 48, 是], [36, 14, 0, 是], [36, 16, 2, 是], [36, 18, 4, 是], [36, 20, 6, 是], [36, 22, 8, 是], [36, 24, 10, 是], [36, 26, 12, 是], [36, 28, 14, 是], [36, 30, 16, 是], [36, 32, 18, 是], [36, 34, 20, 是], [36, 36, 22, 是], [36, 38, 24, 是], [36, 40, 26, 是], [36, 42, 28, 是], [36, 44, 30, 是], [36, 46, 32, 是], [36, 48, 34, 是], [38, 0, 38, 是], [38, 2, 40, 是], [38, 4, 42, 是], [38, 6, 44, 是], [38, 8, 46, 是], [38, 10, 48, 是], [38, 12, 0, 是], [38, 14, 2, 是], [38, 16, 4, 是], [38, 18, 6, 是], [38, 20, 8, 是], [38, 22, 10, 是], [38, 24, 12, 是], [38, 26, 14, 是], [38, 28, 16, 是], [38, 30, 18, 是], [38, 32, 20, 是], [38, 34, 22, 是], [38, 36, 24, 是], [38, 38, 26, 是], [38, 40, 28, 是], [38, 42, 30, 是], [38, 44, 32, 是], [38, 46, 34, 是], [38, 48, 36, 是], [40, 0, 40, 是], [40, 2, 42, 是], [40, 4, 44, 是], [40, 6, 46, 是], [40, 8, 48, 是], [40, 10, 0, 是], [40, 12, 2, 是], [40, 14, 4, 是], [40, 16, 6, 是], [40, 18, 8, 是], [40, 20, 10, 是], [40, 22, 12, 是], [40, 24, 14, 是], [40, 26, 16, 是], [40, 28, 18, 是], [40, 30, 20, 是], [40, 32, 22, 是], [40, 34, 24, 是], [40, 36, 26, 是], [40, 38, 28, 是], [40, 40, 30, 是], [40, 42, 32, 是], [40, 44, 34, 是], [40, 46, 36, 是], [40, 48, 38, 是], [42, 0, 42, 是], [42, 2, 44, 是], [42, 4, 46, 是], [42, 6, 48, 是], [42, 8, 0, 是], [42, 10, 2, 是], [42, 12, 4, 是], [42, 14, 6, 是], [42, 16, 8, 是], [42, 18, 10, 是], [42, 20, 12, 是], [42, 22, 14, 是], [42, 24, 16, 是], [42, 26, 18, 是], [42, 28, 20, 是], [42, 30, 22, 是], [42, 32, 24, 是], [42, 34, 26, 是], [42, 36, 28, 是], [42, 38, 30, 是], [42, 40, 32, 是], [42, 42, 34, 是], [42, 44, 36, 是], [42, 46, 38, 是], [42, 48, 40, 是], [44, 0, 44, 是], [44, 2, 46, 是], [44, 4, 48, 是], [44, 6, 0, 是], [44, 8, 2, 是], [44, 10, 4, 是], [44, 12, 6, 是], [44, 14, 8, 是], [44, 16, 10, 是], [44, 18, 12, 是], [44, 20, 14, 是], [44, 22, 16, 是], [44, 24, 18, 是], [44, 26, 20, 是], [44, 28, 22, 是], [44, 30, 24, 是], [44, 32, 26, 是], [44, 34, 28, 是], [44, 36, 30, 是], [44, 38, 32, 是], [44, 40, 34, 是], [44, 42, 36, 是], [44, 44, 38, 是], [44, 46, 40, 是], [44, 48, 42, 是], [46, 0, 46, 是], [46, 2, 48, 是], [46, 4, 0, 是], [46, 6, 2, 是], [46, 8, 4, 是], [46, 10, 6, 是], [46, 12, 8, 是], [46, 14, 10, 是], [46, 16, 12, 是], [46, 18, 14, 是], [46, 20, 16, 是], [46, 22, 18, 是], [46, 24, 20, 是], [46, 26, 22, 是], [46, 28, 24, 是], [46, 30, 26, 是], [46, 32, 28, 是], [46, 34, 30, 是], [46, 36, 32, 是], [46, 38, 34, 是], [46, 40, 36, 是], [46, 42, 38, 是], [46, 44, 40, 是], [46, 46, 42, 是], [46, 48, 44, 是], [48, 0, 48, 是], [48, 2, 0, 是], [48, 4, 2, 是], [48, 6, 4, 是], [48, 8, 6, 是], [48, 10, 8, 是], [48, 12, 10, 是], [48, 14, 12, 是], [48, 16, 14, 是], [48, 18, 16, 是], [48, 20, 18, 是], [48, 22, 20, 是], [48, 24, 22, 是], [48, 26, 24, 是], [48, 28, 26, 是], [48, 30, 28, 是], [48, 32, 30, 是], [48, 34, 32, 是], [48, 36, 34, 是], [48, 38, 36, 是], [48, 40, 38, 是], [48, 42, 40, 是], [48, 44, 42, 是], [48, 46, 44, 是], [48, 48, 46, 是]], [[0, 0, 是], [2, 48, 是], [4, 46, 是], [6, 44, 是], [8, 42, 是], [10, 40, 是], [12, 38, 是], [14, 36, 是], [16, 34, 是], [18, 32, 是], [20, 30, 是], [22, 28, 是], [24, 26, 是], [26, 24, 是], [28, 22, 是], [30, 20, 是], [32, 18, 是], [34, 16, 是], [36, 14, 是], [38, 12, 是], [40, 10, 是], [42, 8, 是], [44, 6, 是], [46, 4, 是], [48, 2, 是]], 是, [[0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [2, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [3, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [4, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [5, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [6, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [7, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [8, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [9, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [10, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [11, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [12, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [13, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [14, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [15, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [16, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [17, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [18, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [19, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [20, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [21, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [22, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [23, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [24, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [25, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [26, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [27, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [28, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [29, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [30, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [31, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [32, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [33, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [34, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [35, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [36, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [37, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [38, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [39, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [40, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [41, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [42, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [43, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [44, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [45, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [46, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [47, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [48, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]], [49, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]]], 是] 條件：無 先含identity、全product與inverse closure成真subgroup；再對所有g核共軛H。positive branches須normal，boundary須真正nonnormal，不混同未成subgroup。 步驟識別與依賴規則：Quotient_genuine_subgroup_before_actual_normality · 依賴：G001, S003 S005 · implies操作前 source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [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, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]] 操作後 derived = [[[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 是] 條件：無 每個元素g在gH中；若aH交bH，ah1=bh2給b^-1a∈H，從而兩完整coset相同。列全g後去重且依來源排序，元素是coset SETS，不是最小代表元本身。 步驟識別與依賴規則：Quotient_ALL_LEFT_coset_SETS_complete_disjoint_partition · 依賴：G001, S004 S006 · implies操作前 source roles = [0, 0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]] 操作後 derived = [[[0, 0, 0, 0], [0, 2, 2, 0], [0, 4, 4, 0], [0, 6, 6, 0], [0, 8, 8, 0], [0, 10, 10, 0], [0, 12, 12, 0], [0, 14, 14, 0], [0, 16, 16, 0], [0, 18, 18, 0], [0, 20, 20, 0], [0, 22, 22, 0], [0, 24, 24, 0], [0, 26, 26, 0], [0, 28, 28, 0], [0, 30, 30, 0], [0, 32, 32, 0], [0, 34, 34, 0], [0, 36, 36, 0], [0, 38, 38, 0], [0, 40, 40, 0], [0, 42, 42, 0], [0, 44, 44, 0], [0, 46, 46, 0], [0, 48, 48, 0], [2, 0, 2, 0], [2, 2, 4, 0], [2, 4, 6, 0], [2, 6, 8, 0], [2, 8, 10, 0], [2, 10, 12, 0], [2, 12, 14, 0], [2, 14, 16, 0], [2, 16, 18, 0], [2, 18, 20, 0], [2, 20, 22, 0], [2, 22, 24, 0], [2, 24, 26, 0], [2, 26, 28, 0], [2, 28, 30, 0], [2, 30, 32, 0], [2, 32, 34, 0], [2, 34, 36, 0], [2, 36, 38, 0], [2, 38, 40, 0], [2, 40, 42, 0], [2, 42, 44, 0], [2, 44, 46, 0], [2, 46, 48, 0], [2, 48, 0, 0], [4, 0, 4, 0], [4, 2, 6, 0], [4, 4, 8, 0], [4, 6, 10, 0], [4, 8, 12, 0], [4, 10, 14, 0], [4, 12, 16, 0], [4, 14, 18, 0], [4, 16, 20, 0], [4, 18, 22, 0], [4, 20, 24, 0], [4, 22, 26, 0], [4, 24, 28, 0], [4, 26, 30, 0], [4, 28, 32, 0], [4, 30, 34, 0], [4, 32, 36, 0], [4, 34, 38, 0], [4, 36, 40, 0], [4, 38, 42, 0], [4, 40, 44, 0], [4, 42, 46, 0], [4, 44, 48, 0], [4, 46, 0, 0], [4, 48, 2, 0], [6, 0, 6, 0], [6, 2, 8, 0], [6, 4, 10, 0], [6, 6, 12, 0], [6, 8, 14, 0], [6, 10, 16, 0], [6, 12, 18, 0], [6, 14, 20, 0], [6, 16, 22, 0], [6, 18, 24, 0], [6, 20, 26, 0], [6, 22, 28, 0], [6, 24, 30, 0], [6, 26, 32, 0], [6, 28, 34, 0], [6, 30, 36, 0], [6, 32, 38, 0], [6, 34, 40, 0], [6, 36, 42, 0], [6, 38, 44, 0], [6, 40, 46, 0], [6, 42, 48, 0], [6, 44, 0, 0], [6, 46, 2, 0], [6, 48, 4, 0], [8, 0, 8, 0], [8, 2, 10, 0], [8, 4, 12, 0], [8, 6, 14, 0], [8, 8, 16, 0], [8, 10, 18, 0], [8, 12, 20, 0], [8, 14, 22, 0], [8, 16, 24, 0], [8, 18, 26, 0], [8, 20, 28, 0], [8, 22, 30, 0], [8, 24, 32, 0], [8, 26, 34, 0], [8, 28, 36, 0], [8, 30, 38, 0], [8, 32, 40, 0], [8, 34, 42, 0], [8, 36, 44, 0], [8, 38, 46, 0], [8, 40, 48, 0], [8, 42, 0, 0], [8, 44, 2, 0], [8, 46, 4, 0], [8, 48, 6, 0], [10, 0, 10, 0], [10, 2, 12, 0], [10, 4, 14, 0], [10, 6, 16, 0], [10, 8, 18, 0], [10, 10, 20, 0], [10, 12, 22, 0], [10, 14, 24, 0], [10, 16, 26, 0], [10, 18, 28, 0], [10, 20, 30, 0], [10, 22, 32, 0], [10, 24, 34, 0], [10, 26, 36, 0], [10, 28, 38, 0], [10, 30, 40, 0], [10, 32, 42, 0], [10, 34, 44, 0], [10, 36, 46, 0], [10, 38, 48, 0], [10, 40, 0, 0], [10, 42, 2, 0], [10, 44, 4, 0], [10, 46, 6, 0], [10, 48, 8, 0], [12, 0, 12, 0], [12, 2, 14, 0], [12, 4, 16, 0], [12, 6, 18, 0], [12, 8, 20, 0], [12, 10, 22, 0], [12, 12, 24, 0], [12, 14, 26, 0], [12, 16, 28, 0], [12, 18, 30, 0], [12, 20, 32, 0], [12, 22, 34, 0], [12, 24, 36, 0], [12, 26, 38, 0], [12, 28, 40, 0], [12, 30, 42, 0], [12, 32, 44, 0], [12, 34, 46, 0], [12, 36, 48, 0], [12, 38, 0, 0], [12, 40, 2, 0], [12, 42, 4, 0], [12, 44, 6, 0], [12, 46, 8, 0], [12, 48, 10, 0], [14, 0, 14, 0], [14, 2, 16, 0], [14, 4, 18, 0], [14, 6, 20, 0], [14, 8, 22, 0], [14, 10, 24, 0], [14, 12, 26, 0], [14, 14, 28, 0], [14, 16, 30, 0], [14, 18, 32, 0], [14, 20, 34, 0], [14, 22, 36, 0], [14, 24, 38, 0], [14, 26, 40, 0], [14, 28, 42, 0], [14, 30, 44, 0], [14, 32, 46, 0], [14, 34, 48, 0], [14, 36, 0, 0], [14, 38, 2, 0], [14, 40, 4, 0], [14, 42, 6, 0], [14, 44, 8, 0], [14, 46, 10, 0], [14, 48, 12, 0], [16, 0, 16, 0], [16, 2, 18, 0], [16, 4, 20, 0], [16, 6, 22, 0], [16, 8, 24, 0], [16, 10, 26, 0], [16, 12, 28, 0], [16, 14, 30, 0], [16, 16, 32, 0], [16, 18, 34, 0], [16, 20, 36, 0], [16, 22, 38, 0], [16, 24, 40, 0], [16, 26, 42, 0], [16, 28, 44, 0], [16, 30, 46, 0], [16, 32, 48, 0], [16, 34, 0, 0], [16, 36, 2, 0], [16, 38, 4, 0], [16, 40, 6, 0], [16, 42, 8, 0], [16, 44, 10, 0], [16, 46, 12, 0], [16, 48, 14, 0], [18, 0, 18, 0], [18, 2, 20, 0], [18, 4, 22, 0], [18, 6, 24, 0], [18, 8, 26, 0], [18, 10, 28, 0], [18, 12, 30, 0], [18, 14, 32, 0], [18, 16, 34, 0], [18, 18, 36, 0], [18, 20, 38, 0], [18, 22, 40, 0], [18, 24, 42, 0], [18, 26, 44, 0], [18, 28, 46, 0], [18, 30, 48, 0], [18, 32, 0, 0], [18, 34, 2, 0], [18, 36, 4, 0], [18, 38, 6, 0], [18, 40, 8, 0], [18, 42, 10, 0], [18, 44, 12, 0], [18, 46, 14, 0], [18, 48, 16, 0], [20, 0, 20, 0], [20, 2, 22, 0], [20, 4, 24, 0], [20, 6, 26, 0], [20, 8, 28, 0], [20, 10, 30, 0], [20, 12, 32, 0], [20, 14, 34, 0], [20, 16, 36, 0], [20, 18, 38, 0], [20, 20, 40, 0], [20, 22, 42, 0], [20, 24, 44, 0], [20, 26, 46, 0], [20, 28, 48, 0], [20, 30, 0, 0], [20, 32, 2, 0], [20, 34, 4, 0], [20, 36, 6, 0], [20, 38, 8, 0], [20, 40, 10, 0], [20, 42, 12, 0], [20, 44, 14, 0], [20, 46, 16, 0], [20, 48, 18, 0], [22, 0, 22, 0], [22, 2, 24, 0], [22, 4, 26, 0], [22, 6, 28, 0], [22, 8, 30, 0], [22, 10, 32, 0], [22, 12, 34, 0], [22, 14, 36, 0], [22, 16, 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0], [46, 20, 16, 0], [46, 22, 18, 0], [46, 24, 20, 0], [46, 26, 22, 0], [46, 28, 24, 0], [46, 30, 26, 0], [46, 32, 28, 0], [46, 34, 30, 0], [46, 36, 32, 0], [46, 38, 34, 0], [46, 40, 36, 0], [46, 42, 38, 0], [46, 44, 40, 0], [46, 46, 42, 0], [46, 48, 44, 0], [48, 0, 48, 0], [48, 2, 0, 0], [48, 4, 2, 0], [48, 6, 4, 0], [48, 8, 6, 0], [48, 10, 8, 0], [48, 12, 10, 0], [48, 14, 12, 0], [48, 16, 14, 0], [48, 18, 16, 0], [48, 20, 18, 0], [48, 22, 20, 0], [48, 24, 22, 0], [48, 26, 24, 0], [48, 28, 26, 0], [48, 30, 28, 0], [48, 32, 30, 0], [48, 34, 32, 0], [48, 36, 34, 0], [48, 38, 36, 0], [48, 40, 38, 0], [48, 42, 40, 0], [48, 44, 42, 0], [48, 46, 44, 0], [48, 48, 46, 0]], [0], 是] 條件：無 每組coset的每對代表元都要落在同一product coset，僅用首代表元造表還不足以證良定；保完整可能index集合。 步驟識別與依賴規則：Quotient_EVERY_coset_pair_ALL_representative_products · 依賴：G001, S005 S007 · implies操作前 source roles = [0, 1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]] 操作後 derived = [[[0, 1, 1, 1], [0, 3, 3, 1], [0, 5, 5, 1], [0, 7, 7, 1], [0, 9, 9, 1], [0, 11, 11, 1], [0, 13, 13, 1], [0, 15, 15, 1], [0, 17, 17, 1], [0, 19, 19, 1], [0, 21, 21, 1], [0, 23, 23, 1], [0, 25, 25, 1], [0, 27, 27, 1], [0, 29, 29, 1], [0, 31, 31, 1], [0, 33, 33, 1], [0, 35, 35, 1], [0, 37, 37, 1], [0, 39, 39, 1], [0, 41, 41, 1], [0, 43, 43, 1], [0, 45, 45, 1], [0, 47, 47, 1], [0, 49, 49, 1], [2, 1, 3, 1], [2, 3, 5, 1], [2, 5, 7, 1], [2, 7, 9, 1], [2, 9, 11, 1], [2, 11, 13, 1], [2, 13, 15, 1], [2, 15, 17, 1], [2, 17, 19, 1], [2, 19, 21, 1], [2, 21, 23, 1], [2, 23, 25, 1], [2, 25, 27, 1], [2, 27, 29, 1], [2, 29, 31, 1], [2, 31, 33, 1], [2, 33, 35, 1], [2, 35, 37, 1], [2, 37, 39, 1], [2, 39, 41, 1], [2, 41, 43, 1], [2, 43, 45, 1], [2, 45, 47, 1], [2, 47, 49, 1], [2, 49, 1, 1], [4, 1, 5, 1], [4, 3, 7, 1], [4, 5, 9, 1], [4, 7, 11, 1], [4, 9, 13, 1], [4, 11, 15, 1], [4, 13, 17, 1], [4, 15, 19, 1], [4, 17, 21, 1], [4, 19, 23, 1], [4, 21, 25, 1], [4, 23, 27, 1], [4, 25, 29, 1], [4, 27, 31, 1], [4, 29, 33, 1], [4, 31, 35, 1], [4, 33, 37, 1], [4, 35, 39, 1], [4, 37, 41, 1], [4, 39, 43, 1], [4, 41, 45, 1], [4, 43, 47, 1], [4, 45, 49, 1], [4, 47, 1, 1], [4, 49, 3, 1], [6, 1, 7, 1], [6, 3, 9, 1], [6, 5, 11, 1], [6, 7, 13, 1], [6, 9, 15, 1], [6, 11, 17, 1], [6, 13, 19, 1], [6, 15, 21, 1], [6, 17, 23, 1], [6, 19, 25, 1], [6, 21, 27, 1], [6, 23, 29, 1], [6, 25, 31, 1], [6, 27, 33, 1], [6, 29, 35, 1], [6, 31, 37, 1], [6, 33, 39, 1], [6, 35, 41, 1], [6, 37, 43, 1], [6, 39, 45, 1], [6, 41, 47, 1], [6, 43, 49, 1], [6, 45, 1, 1], [6, 47, 3, 1], [6, 49, 5, 1], [8, 1, 9, 1], [8, 3, 11, 1], [8, 5, 13, 1], [8, 7, 15, 1], [8, 9, 17, 1], [8, 11, 19, 1], [8, 13, 21, 1], [8, 15, 23, 1], [8, 17, 25, 1], [8, 19, 27, 1], [8, 21, 29, 1], [8, 23, 31, 1], [8, 25, 33, 1], [8, 27, 35, 1], [8, 29, 37, 1], [8, 31, 39, 1], [8, 33, 41, 1], [8, 35, 43, 1], [8, 37, 45, 1], [8, 39, 47, 1], [8, 41, 49, 1], [8, 43, 1, 1], [8, 45, 3, 1], 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49, 31, 1], [34, 1, 35, 1], [34, 3, 37, 1], [34, 5, 39, 1], [34, 7, 41, 1], [34, 9, 43, 1], [34, 11, 45, 1], [34, 13, 47, 1], [34, 15, 49, 1], [34, 17, 1, 1], [34, 19, 3, 1], [34, 21, 5, 1], [34, 23, 7, 1], [34, 25, 9, 1], [34, 27, 11, 1], [34, 29, 13, 1], [34, 31, 15, 1], [34, 33, 17, 1], [34, 35, 19, 1], [34, 37, 21, 1], [34, 39, 23, 1], [34, 41, 25, 1], [34, 43, 27, 1], [34, 45, 29, 1], [34, 47, 31, 1], [34, 49, 33, 1], [36, 1, 37, 1], [36, 3, 39, 1], [36, 5, 41, 1], [36, 7, 43, 1], [36, 9, 45, 1], [36, 11, 47, 1], [36, 13, 49, 1], [36, 15, 1, 1], [36, 17, 3, 1], [36, 19, 5, 1], [36, 21, 7, 1], [36, 23, 9, 1], [36, 25, 11, 1], [36, 27, 13, 1], [36, 29, 15, 1], [36, 31, 17, 1], [36, 33, 19, 1], [36, 35, 21, 1], [36, 37, 23, 1], [36, 39, 25, 1], [36, 41, 27, 1], [36, 43, 29, 1], [36, 45, 31, 1], [36, 47, 33, 1], [36, 49, 35, 1], [38, 1, 39, 1], [38, 3, 41, 1], [38, 5, 43, 1], [38, 7, 45, 1], [38, 9, 47, 1], [38, 11, 49, 1], [38, 13, 1, 1], [38, 15, 3, 1], [38, 17, 5, 1], [38, 19, 7, 1], [38, 21, 9, 1], [38, 23, 11, 1], [38, 25, 13, 1], [38, 27, 15, 1], [38, 29, 17, 1], [38, 31, 19, 1], [38, 33, 21, 1], [38, 35, 23, 1], [38, 37, 25, 1], [38, 39, 27, 1], [38, 41, 29, 1], [38, 43, 31, 1], [38, 45, 33, 1], [38, 47, 35, 1], [38, 49, 37, 1], [40, 1, 41, 1], [40, 3, 43, 1], [40, 5, 45, 1], [40, 7, 47, 1], [40, 9, 49, 1], [40, 11, 1, 1], [40, 13, 3, 1], [40, 15, 5, 1], [40, 17, 7, 1], [40, 19, 9, 1], [40, 21, 11, 1], [40, 23, 13, 1], [40, 25, 15, 1], [40, 27, 17, 1], [40, 29, 19, 1], [40, 31, 21, 1], [40, 33, 23, 1], [40, 35, 25, 1], [40, 37, 27, 1], [40, 39, 29, 1], [40, 41, 31, 1], [40, 43, 33, 1], [40, 45, 35, 1], [40, 47, 37, 1], [40, 49, 39, 1], [42, 1, 43, 1], [42, 3, 45, 1], [42, 5, 47, 1], [42, 7, 49, 1], [42, 9, 1, 1], [42, 11, 3, 1], [42, 13, 5, 1], [42, 15, 7, 1], [42, 17, 9, 1], [42, 19, 11, 1], [42, 21, 13, 1], [42, 23, 15, 1], [42, 25, 17, 1], [42, 27, 19, 1], [42, 29, 21, 1], [42, 31, 23, 1], [42, 33, 25, 1], [42, 35, 27, 1], [42, 37, 29, 1], [42, 39, 31, 1], [42, 41, 33, 1], [42, 43, 35, 1], [42, 45, 37, 1], [42, 47, 39, 1], [42, 49, 41, 1], [44, 1, 45, 1], [44, 3, 47, 1], [44, 5, 49, 1], [44, 7, 1, 1], [44, 9, 3, 1], [44, 11, 5, 1], [44, 13, 7, 1], [44, 15, 9, 1], [44, 17, 11, 1], [44, 19, 13, 1], [44, 21, 15, 1], [44, 23, 17, 1], [44, 25, 19, 1], [44, 27, 21, 1], [44, 29, 23, 1], [44, 31, 25, 1], [44, 33, 27, 1], [44, 35, 29, 1], [44, 37, 31, 1], [44, 39, 33, 1], [44, 41, 35, 1], [44, 43, 37, 1], [44, 45, 39, 1], [44, 47, 41, 1], [44, 49, 43, 1], [46, 1, 47, 1], [46, 3, 49, 1], [46, 5, 1, 1], [46, 7, 3, 1], [46, 9, 5, 1], [46, 11, 7, 1], [46, 13, 9, 1], [46, 15, 11, 1], [46, 17, 13, 1], [46, 19, 15, 1], [46, 21, 17, 1], [46, 23, 19, 1], [46, 25, 21, 1], [46, 27, 23, 1], [46, 29, 25, 1], [46, 31, 27, 1], [46, 33, 29, 1], [46, 35, 31, 1], [46, 37, 33, 1], [46, 39, 35, 1], [46, 41, 37, 1], [46, 43, 39, 1], [46, 45, 41, 1], [46, 47, 43, 1], [46, 49, 45, 1], [48, 1, 49, 1], [48, 3, 1, 1], [48, 5, 3, 1], [48, 7, 5, 1], [48, 9, 7, 1], [48, 11, 9, 1], [48, 13, 11, 1], [48, 15, 13, 1], [48, 17, 15, 1], [48, 19, 17, 1], [48, 21, 19, 1], [48, 23, 21, 1], [48, 25, 23, 1], [48, 27, 25, 1], [48, 29, 27, 1], [48, 31, 29, 1], [48, 33, 31, 1], [48, 35, 33, 1], [48, 37, 35, 1], [48, 39, 37, 1], [48, 41, 39, 1], [48, 43, 41, 1], [48, 45, 43, 1], [48, 47, 45, 1], [48, 49, 47, 1]], [1], 是] 條件：無 每組coset的每對代表元都要落在同一product coset，僅用首代表元造表還不足以證良定；保完整可能index集合。 步驟識別與依賴規則：Quotient_EVERY_coset_pair_ALL_representative_products · 依賴：G001, S006 S008 · implies操作前 source roles = [1, 0, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48]] 操作後 derived = [[[1, 0, 1, 1], [1, 2, 3, 1], [1, 4, 5, 1], [1, 6, 7, 1], [1, 8, 9, 1], [1, 10, 11, 1], [1, 12, 13, 1], [1, 14, 15, 1], [1, 16, 17, 1], [1, 18, 19, 1], [1, 20, 21, 1], [1, 22, 23, 1], [1, 24, 25, 1], [1, 26, 27, 1], [1, 28, 29, 1], [1, 30, 31, 1], [1, 32, 33, 1], [1, 34, 35, 1], [1, 36, 37, 1], [1, 38, 39, 1], [1, 40, 41, 1], [1, 42, 43, 1], [1, 44, 45, 1], [1, 46, 47, 1], [1, 48, 49, 1], [3, 0, 3, 1], [3, 2, 5, 1], [3, 4, 7, 1], [3, 6, 9, 1], [3, 8, 11, 1], [3, 10, 13, 1], [3, 12, 15, 1], [3, 14, 17, 1], [3, 16, 19, 1], [3, 18, 21, 1], [3, 20, 23, 1], [3, 22, 25, 1], [3, 24, 27, 1], [3, 26, 29, 1], [3, 28, 31, 1], [3, 30, 33, 1], [3, 32, 35, 1], [3, 34, 37, 1], [3, 36, 39, 1], [3, 38, 41, 1], [3, 40, 43, 1], [3, 42, 45, 1], [3, 44, 47, 1], [3, 46, 49, 1], [3, 48, 1, 1], [5, 0, 5, 1], [5, 2, 7, 1], [5, 4, 9, 1], [5, 6, 11, 1], [5, 8, 13, 1], [5, 10, 15, 1], [5, 12, 17, 1], [5, 14, 19, 1], [5, 16, 21, 1], [5, 18, 23, 1], [5, 20, 25, 1], [5, 22, 27, 1], [5, 24, 29, 1], [5, 26, 31, 1], [5, 28, 33, 1], [5, 30, 35, 1], [5, 32, 37, 1], [5, 34, 39, 1], [5, 36, 41, 1], [5, 38, 43, 1], [5, 40, 45, 1], [5, 42, 47, 1], [5, 44, 49, 1], [5, 46, 1, 1], [5, 48, 3, 1], [7, 0, 7, 1], [7, 2, 9, 1], [7, 4, 11, 1], [7, 6, 13, 1], [7, 8, 15, 1], [7, 10, 17, 1], [7, 12, 19, 1], [7, 14, 21, 1], [7, 16, 23, 1], [7, 18, 25, 1], [7, 20, 27, 1], [7, 22, 29, 1], [7, 24, 31, 1], [7, 26, 33, 1], [7, 28, 35, 1], [7, 30, 37, 1], [7, 32, 39, 1], [7, 34, 41, 1], [7, 36, 43, 1], [7, 38, 45, 1], [7, 40, 47, 1], [7, 42, 49, 1], [7, 44, 1, 1], [7, 46, 3, 1], [7, 48, 5, 1], [9, 0, 9, 1], [9, 2, 11, 1], [9, 4, 13, 1], [9, 6, 15, 1], [9, 8, 17, 1], [9, 10, 19, 1], [9, 12, 21, 1], [9, 14, 23, 1], [9, 16, 25, 1], [9, 18, 27, 1], [9, 20, 29, 1], [9, 22, 31, 1], [9, 24, 33, 1], [9, 26, 35, 1], [9, 28, 37, 1], [9, 30, 39, 1], [9, 32, 41, 1], [9, 34, 43, 1], [9, 36, 45, 1], [9, 38, 47, 1], [9, 40, 49, 1], [9, 42, 1, 1], [9, 44, 3, 1], [9, 46, 5, 1], [9, 48, 7, 1], [11, 0, 11, 1], [11, 2, 13, 1], [11, 4, 15, 1], [11, 6, 17, 1], [11, 8, 19, 1], [11, 10, 21, 1], [11, 12, 23, 1], [11, 14, 25, 1], [11, 16, 27, 1], [11, 18, 29, 1], [11, 20, 31, 1], [11, 22, 33, 1], [11, 24, 35, 1], [11, 26, 37, 1], [11, 28, 39, 1], [11, 30, 41, 1], [11, 32, 43, 1], [11, 34, 45, 1], [11, 36, 47, 1], [11, 38, 49, 1], [11, 40, 1, 1], [11, 42, 3, 1], [11, 44, 5, 1], [11, 46, 7, 1], [11, 48, 9, 1], [13, 0, 13, 1], [13, 2, 15, 1], [13, 4, 17, 1], [13, 6, 19, 1], [13, 8, 21, 1], [13, 10, 23, 1], [13, 12, 25, 1], [13, 14, 27, 1], [13, 16, 29, 1], [13, 18, 31, 1], [13, 20, 33, 1], [13, 22, 35, 1], [13, 24, 37, 1], [13, 26, 39, 1], [13, 28, 41, 1], [13, 30, 43, 1], [13, 32, 45, 1], [13, 34, 47, 1], [13, 36, 49, 1], [13, 38, 1, 1], [13, 40, 3, 1], [13, 42, 5, 1], [13, 44, 7, 1], [13, 46, 9, 1], [13, 48, 11, 1], [15, 0, 15, 1], [15, 2, 17, 1], [15, 4, 19, 1], [15, 6, 21, 1], [15, 8, 23, 1], [15, 10, 25, 1], [15, 12, 27, 1], [15, 14, 29, 1], [15, 16, 31, 1], [15, 18, 33, 1], [15, 20, 35, 1], [15, 22, 37, 1], [15, 24, 39, 1], [15, 26, 41, 1], [15, 28, 43, 1], [15, 30, 45, 1], [15, 32, 47, 1], [15, 34, 49, 1], [15, 36, 1, 1], [15, 38, 3, 1], [15, 40, 5, 1], [15, 42, 7, 1], [15, 44, 9, 1], [15, 46, 11, 1], [15, 48, 13, 1], [17, 0, 17, 1], [17, 2, 19, 1], [17, 4, 21, 1], [17, 6, 23, 1], [17, 8, 25, 1], [17, 10, 27, 1], [17, 12, 29, 1], [17, 14, 31, 1], [17, 16, 33, 1], [17, 18, 35, 1], [17, 20, 37, 1], [17, 22, 39, 1], [17, 24, 41, 1], [17, 26, 43, 1], [17, 28, 45, 1], [17, 30, 47, 1], [17, 32, 49, 1], [17, 34, 1, 1], [17, 36, 3, 1], [17, 38, 5, 1], [17, 40, 7, 1], [17, 42, 9, 1], [17, 44, 11, 1], [17, 46, 13, 1], [17, 48, 15, 1], [19, 0, 19, 1], [19, 2, 21, 1], [19, 4, 23, 1], [19, 6, 25, 1], [19, 8, 27, 1], [19, 10, 29, 1], [19, 12, 31, 1], [19, 14, 33, 1], [19, 16, 35, 1], [19, 18, 37, 1], [19, 20, 39, 1], [19, 22, 41, 1], [19, 24, 43, 1], [19, 26, 45, 1], [19, 28, 47, 1], [19, 30, 49, 1], [19, 32, 1, 1], [19, 34, 3, 1], [19, 36, 5, 1], [19, 38, 7, 1], [19, 40, 9, 1], [19, 42, 11, 1], [19, 44, 13, 1], [19, 46, 15, 1], [19, 48, 17, 1], [21, 0, 21, 1], [21, 2, 23, 1], [21, 4, 25, 1], [21, 6, 27, 1], [21, 8, 29, 1], [21, 10, 31, 1], [21, 12, 33, 1], [21, 14, 35, 1], [21, 16, 37, 1], [21, 18, 39, 1], [21, 20, 41, 1], [21, 22, 43, 1], [21, 24, 45, 1], [21, 26, 47, 1], [21, 28, 49, 1], [21, 30, 1, 1], [21, 32, 3, 1], [21, 34, 5, 1], [21, 36, 7, 1], [21, 38, 9, 1], [21, 40, 11, 1], [21, 42, 13, 1], [21, 44, 15, 1], [21, 46, 17, 1], [21, 48, 19, 1], [23, 0, 23, 1], [23, 2, 25, 1], [23, 4, 27, 1], [23, 6, 29, 1], [23, 8, 31, 1], [23, 10, 33, 1], [23, 12, 35, 1], [23, 14, 37, 1], [23, 16, 39, 1], [23, 18, 41, 1], [23, 20, 43, 1], [23, 22, 45, 1], [23, 24, 47, 1], [23, 26, 49, 1], [23, 28, 1, 1], [23, 30, 3, 1], [23, 32, 5, 1], [23, 34, 7, 1], [23, 36, 9, 1], [23, 38, 11, 1], [23, 40, 13, 1], [23, 42, 15, 1], [23, 44, 17, 1], [23, 46, 19, 1], [23, 48, 21, 1], [25, 0, 25, 1], [25, 2, 27, 1], [25, 4, 29, 1], [25, 6, 31, 1], [25, 8, 33, 1], [25, 10, 35, 1], [25, 12, 37, 1], [25, 14, 39, 1], [25, 16, 41, 1], [25, 18, 43, 1], [25, 20, 45, 1], [25, 22, 47, 1], [25, 24, 49, 1], [25, 26, 1, 1], [25, 28, 3, 1], [25, 30, 5, 1], [25, 32, 7, 1], [25, 34, 9, 1], [25, 36, 11, 1], [25, 38, 13, 1], [25, 40, 15, 1], [25, 42, 17, 1], [25, 44, 19, 1], [25, 46, 21, 1], [25, 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1], [35, 40, 25, 1], [35, 42, 27, 1], [35, 44, 29, 1], [35, 46, 31, 1], [35, 48, 33, 1], [37, 0, 37, 1], [37, 2, 39, 1], [37, 4, 41, 1], [37, 6, 43, 1], [37, 8, 45, 1], [37, 10, 47, 1], [37, 12, 49, 1], [37, 14, 1, 1], [37, 16, 3, 1], [37, 18, 5, 1], [37, 20, 7, 1], [37, 22, 9, 1], [37, 24, 11, 1], [37, 26, 13, 1], [37, 28, 15, 1], [37, 30, 17, 1], [37, 32, 19, 1], [37, 34, 21, 1], [37, 36, 23, 1], [37, 38, 25, 1], [37, 40, 27, 1], [37, 42, 29, 1], [37, 44, 31, 1], [37, 46, 33, 1], [37, 48, 35, 1], [39, 0, 39, 1], [39, 2, 41, 1], [39, 4, 43, 1], [39, 6, 45, 1], [39, 8, 47, 1], [39, 10, 49, 1], [39, 12, 1, 1], [39, 14, 3, 1], [39, 16, 5, 1], [39, 18, 7, 1], [39, 20, 9, 1], [39, 22, 11, 1], [39, 24, 13, 1], [39, 26, 15, 1], [39, 28, 17, 1], [39, 30, 19, 1], [39, 32, 21, 1], [39, 34, 23, 1], [39, 36, 25, 1], [39, 38, 27, 1], [39, 40, 29, 1], [39, 42, 31, 1], [39, 44, 33, 1], [39, 46, 35, 1], [39, 48, 37, 1], [41, 0, 41, 1], [41, 2, 43, 1], [41, 4, 45, 1], [41, 6, 47, 1], [41, 8, 49, 1], 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30, 25, 1], [45, 32, 27, 1], [45, 34, 29, 1], [45, 36, 31, 1], [45, 38, 33, 1], [45, 40, 35, 1], [45, 42, 37, 1], [45, 44, 39, 1], [45, 46, 41, 1], [45, 48, 43, 1], [47, 0, 47, 1], [47, 2, 49, 1], [47, 4, 1, 1], [47, 6, 3, 1], [47, 8, 5, 1], [47, 10, 7, 1], [47, 12, 9, 1], [47, 14, 11, 1], [47, 16, 13, 1], [47, 18, 15, 1], [47, 20, 17, 1], [47, 22, 19, 1], [47, 24, 21, 1], [47, 26, 23, 1], [47, 28, 25, 1], [47, 30, 27, 1], [47, 32, 29, 1], [47, 34, 31, 1], [47, 36, 33, 1], [47, 38, 35, 1], [47, 40, 37, 1], [47, 42, 39, 1], [47, 44, 41, 1], [47, 46, 43, 1], [47, 48, 45, 1], [49, 0, 49, 1], [49, 2, 1, 1], [49, 4, 3, 1], [49, 6, 5, 1], [49, 8, 7, 1], [49, 10, 9, 1], [49, 12, 11, 1], [49, 14, 13, 1], [49, 16, 15, 1], [49, 18, 17, 1], [49, 20, 19, 1], [49, 22, 21, 1], [49, 24, 23, 1], [49, 26, 25, 1], [49, 28, 27, 1], [49, 30, 29, 1], [49, 32, 31, 1], [49, 34, 33, 1], [49, 36, 35, 1], [49, 38, 37, 1], [49, 40, 39, 1], [49, 42, 41, 1], [49, 44, 43, 1], [49, 46, 45, 1], [49, 48, 47, 1]], [1], 是] 條件：無 每組coset的每對代表元都要落在同一product coset，僅用首代表元造表還不足以證良定；保完整可能index集合。 步驟識別與依賴規則：Quotient_EVERY_coset_pair_ALL_representative_products · 依賴：G001, S007 S009 · implies操作前 source roles = [1, 1, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]] 操作後 derived = [[[1, 1, 2, 0], [1, 3, 4, 0], [1, 5, 6, 0], [1, 7, 8, 0], [1, 9, 10, 0], [1, 11, 12, 0], [1, 13, 14, 0], [1, 15, 16, 0], [1, 17, 18, 0], [1, 19, 20, 0], [1, 21, 22, 0], [1, 23, 24, 0], [1, 25, 26, 0], [1, 27, 28, 0], [1, 29, 30, 0], [1, 31, 32, 0], [1, 33, 34, 0], [1, 35, 36, 0], [1, 37, 38, 0], [1, 39, 40, 0], [1, 41, 42, 0], [1, 43, 44, 0], [1, 45, 46, 0], [1, 47, 48, 0], [1, 49, 0, 0], [3, 1, 4, 0], [3, 3, 6, 0], [3, 5, 8, 0], [3, 7, 10, 0], [3, 9, 12, 0], [3, 11, 14, 0], [3, 13, 16, 0], [3, 15, 18, 0], [3, 17, 20, 0], [3, 19, 22, 0], [3, 21, 24, 0], [3, 23, 26, 0], [3, 25, 28, 0], [3, 27, 30, 0], [3, 29, 32, 0], [3, 31, 34, 0], [3, 33, 36, 0], [3, 35, 38, 0], [3, 37, 40, 0], [3, 39, 42, 0], [3, 41, 44, 0], [3, 43, 46, 0], [3, 45, 48, 0], [3, 47, 0, 0], [3, 49, 2, 0], [5, 1, 6, 0], [5, 3, 8, 0], [5, 5, 10, 0], [5, 7, 12, 0], [5, 9, 14, 0], [5, 11, 16, 0], [5, 13, 18, 0], [5, 15, 20, 0], [5, 17, 22, 0], [5, 19, 24, 0], [5, 21, 26, 0], [5, 23, 28, 0], [5, 25, 30, 0], [5, 27, 32, 0], [5, 29, 34, 0], [5, 31, 36, 0], [5, 33, 38, 0], [5, 35, 40, 0], [5, 37, 42, 0], [5, 39, 44, 0], [5, 41, 46, 0], [5, 43, 48, 0], [5, 45, 0, 0], [5, 47, 2, 0], [5, 49, 4, 0], [7, 1, 8, 0], [7, 3, 10, 0], [7, 5, 12, 0], [7, 7, 14, 0], [7, 9, 16, 0], [7, 11, 18, 0], [7, 13, 20, 0], [7, 15, 22, 0], [7, 17, 24, 0], [7, 19, 26, 0], [7, 21, 28, 0], [7, 23, 30, 0], [7, 25, 32, 0], [7, 27, 34, 0], [7, 29, 36, 0], [7, 31, 38, 0], [7, 33, 40, 0], [7, 35, 42, 0], [7, 37, 44, 0], [7, 39, 46, 0], [7, 41, 48, 0], [7, 43, 0, 0], [7, 45, 2, 0], [7, 47, 4, 0], [7, 49, 6, 0], [9, 1, 10, 0], [9, 3, 12, 0], [9, 5, 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1, 44, 0], [43, 3, 46, 0], [43, 5, 48, 0], [43, 7, 0, 0], [43, 9, 2, 0], [43, 11, 4, 0], [43, 13, 6, 0], [43, 15, 8, 0], [43, 17, 10, 0], [43, 19, 12, 0], [43, 21, 14, 0], [43, 23, 16, 0], [43, 25, 18, 0], [43, 27, 20, 0], [43, 29, 22, 0], [43, 31, 24, 0], [43, 33, 26, 0], [43, 35, 28, 0], [43, 37, 30, 0], [43, 39, 32, 0], [43, 41, 34, 0], [43, 43, 36, 0], [43, 45, 38, 0], [43, 47, 40, 0], [43, 49, 42, 0], [45, 1, 46, 0], [45, 3, 48, 0], [45, 5, 0, 0], [45, 7, 2, 0], [45, 9, 4, 0], [45, 11, 6, 0], [45, 13, 8, 0], [45, 15, 10, 0], [45, 17, 12, 0], [45, 19, 14, 0], [45, 21, 16, 0], [45, 23, 18, 0], [45, 25, 20, 0], [45, 27, 22, 0], [45, 29, 24, 0], [45, 31, 26, 0], [45, 33, 28, 0], [45, 35, 30, 0], [45, 37, 32, 0], [45, 39, 34, 0], [45, 41, 36, 0], [45, 43, 38, 0], [45, 45, 40, 0], [45, 47, 42, 0], [45, 49, 44, 0], [47, 1, 48, 0], [47, 3, 0, 0], [47, 5, 2, 0], [47, 7, 4, 0], [47, 9, 6, 0], [47, 11, 8, 0], [47, 13, 10, 0], [47, 15, 12, 0], [47, 17, 14, 0], [47, 19, 16, 0], [47, 21, 18, 0], [47, 23, 20, 0], [47, 25, 22, 0], [47, 27, 24, 0], [47, 29, 26, 0], [47, 31, 28, 0], [47, 33, 30, 0], [47, 35, 32, 0], [47, 37, 34, 0], [47, 39, 36, 0], [47, 41, 38, 0], [47, 43, 40, 0], [47, 45, 42, 0], [47, 47, 44, 0], [47, 49, 46, 0], [49, 1, 0, 0], [49, 3, 2, 0], [49, 5, 4, 0], [49, 7, 6, 0], [49, 9, 8, 0], [49, 11, 10, 0], [49, 13, 12, 0], [49, 15, 14, 0], [49, 17, 16, 0], [49, 19, 18, 0], [49, 21, 20, 0], [49, 23, 22, 0], [49, 25, 24, 0], [49, 27, 26, 0], [49, 29, 28, 0], [49, 31, 30, 0], [49, 33, 32, 0], [49, 35, 34, 0], [49, 37, 36, 0], [49, 39, 38, 0], [49, 41, 40, 0], [49, 43, 42, 0], [49, 45, 44, 0], [49, 47, 46, 0], [49, 49, 48, 0]], [0], 是] 條件：無 每組coset的每對代表元都要落在同一product coset，僅用首代表元造表還不足以證良定；保完整可能index集合。 步驟識別與依賴規則：Quotient_EVERY_coset_pair_ALL_representative_products · 依賴：G001, S008 S010 · implies操作前 source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], 是, [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]]] 操作後 derived = [[[0, 1], [1, 0]], 0, [[0, 0], [1, 1]], 是, 否] 條件：無 若a換ah、b換bk，(ah)(bk)=ab(b^-1hb)k∈abH，normality才保代表元替換不變。associativity由G傳下，eH為identity、a^-1H為inverse。固定No只不自動提供commutativity證書，不說具體cyclic quotient非交換，也不引第一同構定理。 步驟識別與依賴規則：Quotient_GENERAL_normality_representative_replacement_and_group_laws · 依賴：G001, S009 ## 逐步反向核對 - 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, 32, 34, 36, 38, 40, 42, 44, 46, 48], 是, [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]], 是, 2, quotient_elements_are_disjoint_complete_coset_sets_not_representatives) 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。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: beec4a280607329c6bfef0726b352e18728521972f2e23b9bb3dca534a9c16c0 - candidate record SHA-256: 4c07d77452c51d7c34cab4e6195e97321801fe41d47e1ace7d83c7d73a8195bf - semantic review receipt SHA-256: 6212b8b0b3b273f3a514e26ebd17d7e81219c56a8f47e40047ee2b6bf01d1ba3 - question-first witness SHA-256: f32a23d5e1b66c7794c60def58741bcdfacff24f3cdfc9bc48109c8f71543cf3 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r02-finite-quotient-group-0024.json)