Question 25350: Explicit Representative Dependence Blocks This Quotient Multiplication

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Original question and givens
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Result
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R0049-25350 · q-20261015-advance-20261114-r02-finite-quotient-group-0100

Original question and givens

Use complete finite 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, 50, 51, 52, 53], [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, 0, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27], [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, 0, 1, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], [21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [25, 26, 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, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [26, 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, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52], [27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 0, 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], [28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 1, 0, 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], [29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18], [45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19], [46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20], [47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21], [48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22], [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23], [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24], [51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25], [52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 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, 0, 26], [53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 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, 0]], identity=0, explicit subset=[0, 27] and the entire left-coset partition. Subgroup qualification precedes normality. Quotient elements are coset sets, not representatives; coset indices follow the source canonical element-list order. Give (subgroup, normal, cosets, representative_counterexample, well_defined, quotient_group_certificate, boundary).

G001 — Use complete finite 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, 50, 51, 52, 53], [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, 0, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27], [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, 0, 1, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], [21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [25, 26, 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, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [26, 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, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52], [27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 0, 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], [28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 1, 0, 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], [29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18], [45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19], [46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20], [47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21], [48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22], [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23], [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24], [51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25], [52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 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, 0, 26], [53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 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, 0]], identity=0, explicit subset=[0, 27] and the entire left-coset partition. Subgroup qualification precedes normality. Quotient elements are coset sets, not representatives; coset indices follow the source canonical element-list order. Give (subgroup, normal, cosets, representative_counterexample, well_defined, quotient_group_certificate, boundary).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

mko-finite-quotient-group

Step-by-step derivation

S001 · implies

Before

source roles = [quotient-nonnormal-boundary]

After

derived = [[subgroup, normal, cosets, representative_counterexample, well_defined, quotient_group_certificate, boundary]]

Conditions: none

List the full source field order without JavaScript.LP boundary modes all have6 fields but select different roles from the original mode,not answer shape.

Step identifiers and dependencies

Rule: source_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

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, 50, 51, 52, 53], [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, 0, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27], [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, 0, 1, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [19, 20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [20, 21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], [21, 22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [22, 23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [23, 24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [24, 25, 26, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [25, 26, 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, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [26, 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, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52], [27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 0, 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], [28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 1, 0, 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], [29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19, 18], [45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20, 19], [46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21, 20], [47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22, 21], [48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23, 22], [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24, 23], [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25, 24], [51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 26, 25], [52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 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, 0, 26], [53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 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, 0]], 0]

After

derived = [54, [[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], [50, 50, 50, 50], [51, 51, 51, 51], [52, 52, 52, 52], [53, 53, 53, 53]], Yes]

Conditions: none

Validate the complete closed Cayley table and actual identity label,without assuming0 or the old32-element cap.

Step identifiers and dependencies

Rule: Quotient_complete_group_table_actual_identity · Uses: G001, S001

S003 · implies

Before

source roles = [54, 0]

After

derived = [[[Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes]], 157464, [0, 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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]]

Conditions: none

Each pair-matrix entry checks associativity for every z,covering n^3 obligations;each inverse returns the same identity from both sides.This is exhaustive,not sampling.

Step identifiers and dependencies

Rule: Quotient_ALL_group_associativity_triples_and_two_sided_inverses · Uses: G001, S002

S004 · implies

Before

source roles = [0, [0, 27]]

After

derived = [[[0, 0, 0, Yes], [0, 27, 27, Yes], [27, 0, 27, Yes], [27, 27, 0, Yes]], [[0, 0, Yes], [27, 27, Yes]], Yes, [[0, [0, 27]], [1, [0, 29]], [2, [0, 31]], [3, [0, 33]], [4, [0, 35]], [5, [0, 37]], [6, [0, 39]], [7, [0, 41]], [8, [0, 43]], [9, [0, 45]], [10, [0, 47]], [11, [0, 49]], [12, [0, 51]], [13, [0, 53]], [14, [0, 28]], [15, [0, 30]], [16, [0, 32]], [17, [0, 34]], [18, [0, 36]], [19, [0, 38]], [20, [0, 40]], [21, [0, 42]], [22, [0, 44]], [23, [0, 46]], [24, [0, 48]], [25, [0, 50]], [26, [0, 52]], [27, [0, 27]], [28, [0, 29]], [29, [0, 31]], [30, [0, 33]], [31, [0, 35]], [32, [0, 37]], [33, [0, 39]], [34, [0, 41]], [35, [0, 43]], [36, [0, 45]], [37, [0, 47]], [38, [0, 49]], [39, [0, 51]], [40, [0, 53]], [41, [0, 28]], [42, [0, 30]], [43, [0, 32]], [44, [0, 34]], [45, [0, 36]], [46, [0, 38]], [47, [0, 40]], [48, [0, 42]], [49, [0, 44]], [50, [0, 46]], [51, [0, 48]], [52, [0, 50]], [53, [0, 52]]], No]

Conditions: none

First qualify identity,all products and inverse closure as a genuine subgroup,then test conjugation for every g.Positive branches require normality and the boundary requires actual nonnormality,not failed subgroup qualification.

Step identifiers and dependencies

Rule: Quotient_genuine_subgroup_before_actual_normality · Uses: G001, S003

S005 · implies

Before

source roles = [[0, 27], [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, 50, 51, 52, 53]]

After

derived = [[[0, 27], [1, 28], [10, 37], [11, 38], [12, 39], [13, 40], [14, 41], [15, 42], [16, 43], [17, 44], [18, 45], [19, 46], [2, 29], [20, 47], [21, 48], [22, 49], [23, 50], [24, 51], [25, 52], [26, 53], [3, 30], [4, 31], [5, 32], [6, 33], [7, 34], [8, 35], [9, 36]], [0, 1, 12, 20, 21, 22, 23, 24, 25, 26, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 0, 1, 12, 20, 21, 22, 23, 24, 25, 26, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19], Yes]

Conditions: none

Every g belongs to gH.If aH meets bH,ah1=bh2 implies b^-1a in H and the complete cosets coincide.Enumerate every g,deduplicate and retain source order.Quotient elements are coset SETS,not least representatives.

Step identifiers and dependencies

Rule: Quotient_ALL_LEFT_coset_SETS_complete_disjoint_partition · Uses: G001, S004

S006 · implies

Before

source roles = [0, 0, [0, 27], [0, 27]]

After

derived = [[[0, 0, 0, 0], [0, 27, 27, 0], [27, 0, 27, 0], [27, 27, 0, 0]], [0], Yes]

Conditions: none

For every ordered coset pair,all representative products must land in one product coset.A least-representative table alone does not establish well-definedness;retain the complete set of possible indices.

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S005

S007 · implies

Before

source roles = [0, 1, [0, 27], [1, 28]]

After

derived = [[[0, 1, 1, 1], [0, 28, 28, 1], [27, 1, 53, 19], [27, 28, 26, 19]], [1, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S006

S008 · implies

Before

source roles = [0, 2, [0, 27], [10, 37]]

After

derived = [[[0, 10, 10, 2], [0, 37, 37, 2], [27, 10, 44, 9], [27, 37, 17, 9]], [2, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S007

S009 · implies

Before

source roles = [0, 3, [0, 27], [11, 38]]

After

derived = [[[0, 11, 11, 3], [0, 38, 38, 3], [27, 11, 43, 8], [27, 38, 16, 8]], [3, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S008

S010 · implies

Before

source roles = [0, 4, [0, 27], [12, 39]]

After

derived = [[[0, 12, 12, 4], [0, 39, 39, 4], [27, 12, 42, 7], [27, 39, 15, 7]], [4, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S009

S011 · implies

Before

source roles = [0, 5, [0, 27], [13, 40]]

After

derived = [[[0, 13, 13, 5], [0, 40, 40, 5], [27, 13, 41, 6], [27, 40, 14, 6]], [5, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S010

S012 · implies

Before

source roles = [0, 6, [0, 27], [14, 41]]

After

derived = [[[0, 14, 14, 6], [0, 41, 41, 6], [27, 14, 40, 5], [27, 41, 13, 5]], [5, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S011

S013 · implies

Before

source roles = [0, 7, [0, 27], [15, 42]]

After

derived = [[[0, 15, 15, 7], [0, 42, 42, 7], [27, 15, 39, 4], [27, 42, 12, 4]], [4, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S012

S014 · implies

Before

source roles = [0, 8, [0, 27], [16, 43]]

After

derived = [[[0, 16, 16, 8], [0, 43, 43, 8], [27, 16, 38, 3], [27, 43, 11, 3]], [3, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S013

S015 · implies

Before

source roles = [0, 9, [0, 27], [17, 44]]

After

derived = [[[0, 17, 17, 9], [0, 44, 44, 9], [27, 17, 37, 2], [27, 44, 10, 2]], [2, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S014

S016 · implies

Before

source roles = [0, 10, [0, 27], [18, 45]]

After

derived = [[[0, 18, 18, 10], [0, 45, 45, 10], [27, 18, 36, 26], [27, 45, 9, 26]], [10, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S015

S017 · implies

Before

source roles = [0, 11, [0, 27], [19, 46]]

After

derived = [[[0, 19, 19, 11], [0, 46, 46, 11], [27, 19, 35, 25], [27, 46, 8, 25]], [11, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S016

S018 · implies

Before

source roles = [0, 12, [0, 27], [2, 29]]

After

derived = [[[0, 2, 2, 12], [0, 29, 29, 12], [27, 2, 52, 18], [27, 29, 25, 18]], [12, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S017

S019 · implies

Before

source roles = [0, 13, [0, 27], [20, 47]]

After

derived = [[[0, 20, 20, 13], [0, 47, 47, 13], [27, 20, 34, 24], [27, 47, 7, 24]], [13, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S018

S020 · implies

Before

source roles = [0, 14, [0, 27], [21, 48]]

After

derived = [[[0, 21, 21, 14], [0, 48, 48, 14], [27, 21, 33, 23], [27, 48, 6, 23]], [14, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S019

S021 · implies

Before

source roles = [0, 15, [0, 27], [22, 49]]

After

derived = [[[0, 22, 22, 15], [0, 49, 49, 15], [27, 22, 32, 22], [27, 49, 5, 22]], [15, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S020

S022 · implies

Before

source roles = [0, 16, [0, 27], [23, 50]]

After

derived = [[[0, 23, 23, 16], [0, 50, 50, 16], [27, 23, 31, 21], [27, 50, 4, 21]], [16, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S021

S023 · implies

Before

source roles = [0, 17, [0, 27], [24, 51]]

After

derived = [[[0, 24, 24, 17], [0, 51, 51, 17], [27, 24, 30, 20], [27, 51, 3, 20]], [17, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S022

S024 · implies

Before

source roles = [0, 18, [0, 27], [25, 52]]

After

derived = [[[0, 25, 25, 18], [0, 52, 52, 18], [27, 25, 29, 12], [27, 52, 2, 12]], [12, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S023

S025 · implies

Before

source roles = [0, 19, [0, 27], [26, 53]]

After

derived = [[[0, 26, 26, 19], [0, 53, 53, 19], [27, 26, 28, 1], [27, 53, 1, 1]], [1, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S024

S026 · implies

Before

source roles = [0, 20, [0, 27], [3, 30]]

After

derived = [[[0, 3, 3, 20], [0, 30, 30, 20], [27, 3, 51, 17], [27, 30, 24, 17]], [17, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S025

S027 · implies

Before

source roles = [0, 21, [0, 27], [4, 31]]

After

derived = [[[0, 4, 4, 21], [0, 31, 31, 21], [27, 4, 50, 16], [27, 31, 23, 16]], [16, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S026

S028 · implies

Before

source roles = [0, 22, [0, 27], [5, 32]]

After

derived = [[[0, 5, 5, 22], [0, 32, 32, 22], [27, 5, 49, 15], [27, 32, 22, 15]], [15, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S027

S029 · implies

Before

source roles = [0, 23, [0, 27], [6, 33]]

After

derived = [[[0, 6, 6, 23], [0, 33, 33, 23], [27, 6, 48, 14], [27, 33, 21, 14]], [14, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S028

S030 · implies

Before

source roles = [0, 24, [0, 27], [7, 34]]

After

derived = [[[0, 7, 7, 24], [0, 34, 34, 24], [27, 7, 47, 13], [27, 34, 20, 13]], [13, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S029

S031 · implies

Before

source roles = [0, 25, [0, 27], [8, 35]]

After

derived = [[[0, 8, 8, 25], [0, 35, 35, 25], [27, 8, 46, 11], [27, 35, 19, 11]], [11, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S030

S032 · implies

Before

source roles = [0, 26, [0, 27], [9, 36]]

After

derived = [[[0, 9, 9, 26], [0, 36, 36, 26], [27, 9, 45, 10], [27, 36, 18, 10]], [10, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S031

S033 · implies

Before

source roles = [1, 0, [1, 28], [0, 27]]

After

derived = [[[1, 0, 1, 1], [1, 27, 28, 1], [28, 0, 28, 1], [28, 27, 1, 1]], [1], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S032

S034 · implies

Before

source roles = [1, 1, [1, 28], [1, 28]]

After

derived = [[[1, 1, 2, 12], [1, 28, 29, 12], [28, 1, 27, 0], [28, 28, 0, 0]], [0, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S033

S035 · implies

Before

source roles = [1, 2, [1, 28], [10, 37]]

After

derived = [[[1, 10, 11, 3], [1, 37, 38, 3], [28, 10, 45, 10], [28, 37, 18, 10]], [3, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S034

S036 · implies

Before

source roles = [1, 3, [1, 28], [11, 38]]

After

derived = [[[1, 11, 12, 4], [1, 38, 39, 4], [28, 11, 44, 9], [28, 38, 17, 9]], [4, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S035

S037 · implies

Before

source roles = [1, 4, [1, 28], [12, 39]]

After

derived = [[[1, 12, 13, 5], [1, 39, 40, 5], [28, 12, 43, 8], [28, 39, 16, 8]], [5, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S036

S038 · implies

Before

source roles = [1, 5, [1, 28], [13, 40]]

After

derived = [[[1, 13, 14, 6], [1, 40, 41, 6], [28, 13, 42, 7], [28, 40, 15, 7]], [6, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S037

S039 · implies

Before

source roles = [1, 6, [1, 28], [14, 41]]

After

derived = [[[1, 14, 15, 7], [1, 41, 42, 7], [28, 14, 41, 6], [28, 41, 14, 6]], [6, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S038

S040 · implies

Before

source roles = [1, 7, [1, 28], [15, 42]]

After

derived = [[[1, 15, 16, 8], [1, 42, 43, 8], [28, 15, 40, 5], [28, 42, 13, 5]], [5, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S039

S041 · implies

Before

source roles = [1, 8, [1, 28], [16, 43]]

After

derived = [[[1, 16, 17, 9], [1, 43, 44, 9], [28, 16, 39, 4], [28, 43, 12, 4]], [4, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S040

S042 · implies

Before

source roles = [1, 9, [1, 28], [17, 44]]

After

derived = [[[1, 17, 18, 10], [1, 44, 45, 10], [28, 17, 38, 3], [28, 44, 11, 3]], [3, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S041

S043 · implies

Before

source roles = [1, 10, [1, 28], [18, 45]]

After

derived = [[[1, 18, 19, 11], [1, 45, 46, 11], [28, 18, 37, 2], [28, 45, 10, 2]], [2, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S042

S044 · implies

Before

source roles = [1, 11, [1, 28], [19, 46]]

After

derived = [[[1, 19, 20, 13], [1, 46, 47, 13], [28, 19, 36, 26], [28, 46, 9, 26]], [13, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S043

S045 · implies

Before

source roles = [1, 12, [1, 28], [2, 29]]

After

derived = [[[1, 2, 3, 20], [1, 29, 30, 20], [28, 2, 53, 19], [28, 29, 26, 19]], [19, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S044

S046 · implies

Before

source roles = [1, 13, [1, 28], [20, 47]]

After

derived = [[[1, 20, 21, 14], [1, 47, 48, 14], [28, 20, 35, 25], [28, 47, 8, 25]], [14, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S045

S047 · implies

Before

source roles = [1, 14, [1, 28], [21, 48]]

After

derived = [[[1, 21, 22, 15], [1, 48, 49, 15], [28, 21, 34, 24], [28, 48, 7, 24]], [15, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S046

S048 · implies

Before

source roles = [1, 15, [1, 28], [22, 49]]

After

derived = [[[1, 22, 23, 16], [1, 49, 50, 16], [28, 22, 33, 23], [28, 49, 6, 23]], [16, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S047

S049 · implies

Before

source roles = [1, 16, [1, 28], [23, 50]]

After

derived = [[[1, 23, 24, 17], [1, 50, 51, 17], [28, 23, 32, 22], [28, 50, 5, 22]], [17, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S048

S050 · implies

Before

source roles = [1, 17, [1, 28], [24, 51]]

After

derived = [[[1, 24, 25, 18], [1, 51, 52, 18], [28, 24, 31, 21], [28, 51, 4, 21]], [18, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S049

S051 · implies

Before

source roles = [1, 18, [1, 28], [25, 52]]

After

derived = [[[1, 25, 26, 19], [1, 52, 53, 19], [28, 25, 30, 20], [28, 52, 3, 20]], [19, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S050

S052 · implies

Before

source roles = [1, 19, [1, 28], [26, 53]]

After

derived = [[[1, 26, 0, 0], [1, 53, 27, 0], [28, 26, 29, 12], [28, 53, 2, 12]], [0, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S051

S053 · implies

Before

source roles = [1, 20, [1, 28], [3, 30]]

After

derived = [[[1, 3, 4, 21], [1, 30, 31, 21], [28, 3, 52, 18], [28, 30, 25, 18]], [18, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S052

S054 · implies

Before

source roles = [1, 21, [1, 28], [4, 31]]

After

derived = [[[1, 4, 5, 22], [1, 31, 32, 22], [28, 4, 51, 17], [28, 31, 24, 17]], [17, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S053

S055 · implies

Before

source roles = [1, 22, [1, 28], [5, 32]]

After

derived = [[[1, 5, 6, 23], [1, 32, 33, 23], [28, 5, 50, 16], [28, 32, 23, 16]], [16, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S054

S056 · implies

Before

source roles = [1, 23, [1, 28], [6, 33]]

After

derived = [[[1, 6, 7, 24], [1, 33, 34, 24], [28, 6, 49, 15], [28, 33, 22, 15]], [15, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S055

S057 · implies

Before

source roles = [1, 24, [1, 28], [7, 34]]

After

derived = [[[1, 7, 8, 25], [1, 34, 35, 25], [28, 7, 48, 14], [28, 34, 21, 14]], [14, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S056

S058 · implies

Before

source roles = [1, 25, [1, 28], [8, 35]]

After

derived = [[[1, 8, 9, 26], [1, 35, 36, 26], [28, 8, 47, 13], [28, 35, 20, 13]], [13, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S057

S059 · implies

Before

source roles = [1, 26, [1, 28], [9, 36]]

After

derived = [[[1, 9, 10, 2], [1, 36, 37, 2], [28, 9, 46, 11], [28, 36, 19, 11]], [2, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S058

S060 · implies

Before

source roles = [2, 0, [10, 37], [0, 27]]

After

derived = [[[10, 0, 10, 2], [10, 27, 37, 2], [37, 0, 37, 2], [37, 27, 10, 2]], [2], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S059

S061 · implies

Before

source roles = [2, 1, [10, 37], [1, 28]]

After

derived = [[[10, 1, 11, 3], [10, 28, 38, 3], [37, 1, 36, 26], [37, 28, 9, 26]], [3, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S060

S062 · implies

Before

source roles = [2, 2, [10, 37], [10, 37]]

After

derived = [[[10, 10, 20, 13], [10, 37, 47, 13], [37, 10, 27, 0], [37, 37, 0, 0]], [0, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S061

S063 · implies

Before

source roles = [2, 3, [10, 37], [11, 38]]

After

derived = [[[10, 11, 21, 14], [10, 38, 48, 14], [37, 11, 53, 19], [37, 38, 26, 19]], [14, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S062

S064 · implies

Before

source roles = [2, 4, [10, 37], [12, 39]]

After

derived = [[[10, 12, 22, 15], [10, 39, 49, 15], [37, 12, 52, 18], [37, 39, 25, 18]], [15, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S063

S065 · implies

Before

source roles = [2, 5, [10, 37], [13, 40]]

After

derived = [[[10, 13, 23, 16], [10, 40, 50, 16], [37, 13, 51, 17], [37, 40, 24, 17]], [16, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S064

S066 · implies

Before

source roles = [2, 6, [10, 37], [14, 41]]

After

derived = [[[10, 14, 24, 17], [10, 41, 51, 17], [37, 14, 50, 16], [37, 41, 23, 16]], [16, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S065

S067 · implies

Before

source roles = [2, 7, [10, 37], [15, 42]]

After

derived = [[[10, 15, 25, 18], [10, 42, 52, 18], [37, 15, 49, 15], [37, 42, 22, 15]], [15, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S066

S068 · implies

Before

source roles = [2, 8, [10, 37], [16, 43]]

After

derived = [[[10, 16, 26, 19], [10, 43, 53, 19], [37, 16, 48, 14], [37, 43, 21, 14]], [14, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S067

S069 · implies

Before

source roles = [2, 9, [10, 37], [17, 44]]

After

derived = [[[10, 17, 0, 0], [10, 44, 27, 0], [37, 17, 47, 13], [37, 44, 20, 13]], [0, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S068

S070 · implies

Before

source roles = [2, 10, [10, 37], [18, 45]]

After

derived = [[[10, 18, 1, 1], [10, 45, 28, 1], [37, 18, 46, 11], [37, 45, 19, 11]], [1, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S069

S071 · implies

Before

source roles = [2, 11, [10, 37], [19, 46]]

After

derived = [[[10, 19, 2, 12], [10, 46, 29, 12], [37, 19, 45, 10], [37, 46, 18, 10]], [10, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S070

S072 · implies

Before

source roles = [2, 12, [10, 37], [2, 29]]

After

derived = [[[10, 2, 12, 4], [10, 29, 39, 4], [37, 2, 35, 25], [37, 29, 8, 25]], [4, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S071

S073 · implies

Before

source roles = [2, 13, [10, 37], [20, 47]]

After

derived = [[[10, 20, 3, 20], [10, 47, 30, 20], [37, 20, 44, 9], [37, 47, 17, 9]], [9, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S072

S074 · implies

Before

source roles = [2, 14, [10, 37], [21, 48]]

After

derived = [[[10, 21, 4, 21], [10, 48, 31, 21], [37, 21, 43, 8], [37, 48, 16, 8]], [8, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S073

S075 · implies

Before

source roles = [2, 15, [10, 37], [22, 49]]

After

derived = [[[10, 22, 5, 22], [10, 49, 32, 22], [37, 22, 42, 7], [37, 49, 15, 7]], [7, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S074

S076 · implies

Before

source roles = [2, 16, [10, 37], [23, 50]]

After

derived = [[[10, 23, 6, 23], [10, 50, 33, 23], [37, 23, 41, 6], [37, 50, 14, 6]], [6, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S075

S077 · implies

Before

source roles = [2, 17, [10, 37], [24, 51]]

After

derived = [[[10, 24, 7, 24], [10, 51, 34, 24], [37, 24, 40, 5], [37, 51, 13, 5]], [5, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S076

S078 · implies

Before

source roles = [2, 18, [10, 37], [25, 52]]

After

derived = [[[10, 25, 8, 25], [10, 52, 35, 25], [37, 25, 39, 4], [37, 52, 12, 4]], [4, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S077

S079 · implies

Before

source roles = [2, 19, [10, 37], [26, 53]]

After

derived = [[[10, 26, 9, 26], [10, 53, 36, 26], [37, 26, 38, 3], [37, 53, 11, 3]], [3, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S078

S080 · implies

Before

source roles = [2, 20, [10, 37], [3, 30]]

After

derived = [[[10, 3, 13, 5], [10, 30, 40, 5], [37, 3, 34, 24], [37, 30, 7, 24]], [5, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S079

S081 · implies

Before

source roles = [2, 21, [10, 37], [4, 31]]

After

derived = [[[10, 4, 14, 6], [10, 31, 41, 6], [37, 4, 33, 23], [37, 31, 6, 23]], [6, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S080

S082 · implies

Before

source roles = [2, 22, [10, 37], [5, 32]]

After

derived = [[[10, 5, 15, 7], [10, 32, 42, 7], [37, 5, 32, 22], [37, 32, 5, 22]], [7, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S081

S083 · implies

Before

source roles = [2, 23, [10, 37], [6, 33]]

After

derived = [[[10, 6, 16, 8], [10, 33, 43, 8], [37, 6, 31, 21], [37, 33, 4, 21]], [8, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S082

S084 · implies

Before

source roles = [2, 24, [10, 37], [7, 34]]

After

derived = [[[10, 7, 17, 9], [10, 34, 44, 9], [37, 7, 30, 20], [37, 34, 3, 20]], [9, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S083

S085 · implies

Before

source roles = [2, 25, [10, 37], [8, 35]]

After

derived = [[[10, 8, 18, 10], [10, 35, 45, 10], [37, 8, 29, 12], [37, 35, 2, 12]], [10, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S084

S086 · implies

Before

source roles = [2, 26, [10, 37], [9, 36]]

After

derived = [[[10, 9, 19, 11], [10, 36, 46, 11], [37, 9, 28, 1], [37, 36, 1, 1]], [1, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S085

S087 · implies

Before

source roles = [3, 0, [11, 38], [0, 27]]

After

derived = [[[11, 0, 11, 3], [11, 27, 38, 3], [38, 0, 38, 3], [38, 27, 11, 3]], [3], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S086

S088 · implies

Before

source roles = [3, 1, [11, 38], [1, 28]]

After

derived = [[[11, 1, 12, 4], [11, 28, 39, 4], [38, 1, 37, 2], [38, 28, 10, 2]], [2, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S087

S089 · implies

Before

source roles = [3, 2, [11, 38], [10, 37]]

After

derived = [[[11, 10, 21, 14], [11, 37, 48, 14], [38, 10, 28, 1], [38, 37, 1, 1]], [1, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S088

S090 · implies

Before

source roles = [3, 3, [11, 38], [11, 38]]

After

derived = [[[11, 11, 22, 15], [11, 38, 49, 15], [38, 11, 27, 0], [38, 38, 0, 0]], [0, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S089

S091 · implies

Before

source roles = [3, 4, [11, 38], [12, 39]]

After

derived = [[[11, 12, 23, 16], [11, 39, 50, 16], [38, 12, 53, 19], [38, 39, 26, 19]], [16, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S090

S092 · implies

Before

source roles = [3, 5, [11, 38], [13, 40]]

After

derived = [[[11, 13, 24, 17], [11, 40, 51, 17], [38, 13, 52, 18], [38, 40, 25, 18]], [17, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S091

S093 · implies

Before

source roles = [3, 6, [11, 38], [14, 41]]

After

derived = [[[11, 14, 25, 18], [11, 41, 52, 18], [38, 14, 51, 17], [38, 41, 24, 17]], [17, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S092

S094 · implies

Before

source roles = [3, 7, [11, 38], [15, 42]]

After

derived = [[[11, 15, 26, 19], [11, 42, 53, 19], [38, 15, 50, 16], [38, 42, 23, 16]], [16, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S093

S095 · implies

Before

source roles = [3, 8, [11, 38], [16, 43]]

After

derived = [[[11, 16, 0, 0], [11, 43, 27, 0], [38, 16, 49, 15], [38, 43, 22, 15]], [0, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S094

S096 · implies

Before

source roles = [3, 9, [11, 38], [17, 44]]

After

derived = [[[11, 17, 1, 1], [11, 44, 28, 1], [38, 17, 48, 14], [38, 44, 21, 14]], [1, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S095

S097 · implies

Before

source roles = [3, 10, [11, 38], [18, 45]]

After

derived = [[[11, 18, 2, 12], [11, 45, 29, 12], [38, 18, 47, 13], [38, 45, 20, 13]], [12, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S096

S098 · implies

Before

source roles = [3, 11, [11, 38], [19, 46]]

After

derived = [[[11, 19, 3, 20], [11, 46, 30, 20], [38, 19, 46, 11], [38, 46, 19, 11]], [11, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S097

S099 · implies

Before

source roles = [3, 12, [11, 38], [2, 29]]

After

derived = [[[11, 2, 13, 5], [11, 29, 40, 5], [38, 2, 36, 26], [38, 29, 9, 26]], [5, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S098

S100 · implies

Before

source roles = [3, 13, [11, 38], [20, 47]]

After

derived = [[[11, 20, 4, 21], [11, 47, 31, 21], [38, 20, 45, 10], [38, 47, 18, 10]], [10, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S099

S101 · implies

Before

source roles = [3, 14, [11, 38], [21, 48]]

After

derived = [[[11, 21, 5, 22], [11, 48, 32, 22], [38, 21, 44, 9], [38, 48, 17, 9]], [9, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S100

S102 · implies

Before

source roles = [3, 15, [11, 38], [22, 49]]

After

derived = [[[11, 22, 6, 23], [11, 49, 33, 23], [38, 22, 43, 8], [38, 49, 16, 8]], [8, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S101

S103 · implies

Before

source roles = [3, 16, [11, 38], [23, 50]]

After

derived = [[[11, 23, 7, 24], [11, 50, 34, 24], [38, 23, 42, 7], [38, 50, 15, 7]], [7, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S102

S104 · implies

Before

source roles = [3, 17, [11, 38], [24, 51]]

After

derived = [[[11, 24, 8, 25], [11, 51, 35, 25], [38, 24, 41, 6], [38, 51, 14, 6]], [6, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S103

S105 · implies

Before

source roles = [3, 18, [11, 38], [25, 52]]

After

derived = [[[11, 25, 9, 26], [11, 52, 36, 26], [38, 25, 40, 5], [38, 52, 13, 5]], [5, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S104

S106 · implies

Before

source roles = [3, 19, [11, 38], [26, 53]]

After

derived = [[[11, 26, 10, 2], [11, 53, 37, 2], [38, 26, 39, 4], [38, 53, 12, 4]], [2, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S105

S107 · implies

Before

source roles = [3, 20, [11, 38], [3, 30]]

After

derived = [[[11, 3, 14, 6], [11, 30, 41, 6], [38, 3, 35, 25], [38, 30, 8, 25]], [6, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S106

S108 · implies

Before

source roles = [3, 21, [11, 38], [4, 31]]

After

derived = [[[11, 4, 15, 7], [11, 31, 42, 7], [38, 4, 34, 24], [38, 31, 7, 24]], [7, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S107

S109 · implies

Before

source roles = [3, 22, [11, 38], [5, 32]]

After

derived = [[[11, 5, 16, 8], [11, 32, 43, 8], [38, 5, 33, 23], [38, 32, 6, 23]], [8, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S108

S110 · implies

Before

source roles = [3, 23, [11, 38], [6, 33]]

After

derived = [[[11, 6, 17, 9], [11, 33, 44, 9], [38, 6, 32, 22], [38, 33, 5, 22]], [9, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S109

S111 · implies

Before

source roles = [3, 24, [11, 38], [7, 34]]

After

derived = [[[11, 7, 18, 10], [11, 34, 45, 10], [38, 7, 31, 21], [38, 34, 4, 21]], [10, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S110

S112 · implies

Before

source roles = [3, 25, [11, 38], [8, 35]]

After

derived = [[[11, 8, 19, 11], [11, 35, 46, 11], [38, 8, 30, 20], [38, 35, 3, 20]], [11, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S111

S113 · implies

Before

source roles = [3, 26, [11, 38], [9, 36]]

After

derived = [[[11, 9, 20, 13], [11, 36, 47, 13], [38, 9, 29, 12], [38, 36, 2, 12]], [12, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S112

S114 · implies

Before

source roles = [4, 0, [12, 39], [0, 27]]

After

derived = [[[12, 0, 12, 4], [12, 27, 39, 4], [39, 0, 39, 4], [39, 27, 12, 4]], [4], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S113

S115 · implies

Before

source roles = [4, 1, [12, 39], [1, 28]]

After

derived = [[[12, 1, 13, 5], [12, 28, 40, 5], [39, 1, 38, 3], [39, 28, 11, 3]], [3, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S114

S116 · implies

Before

source roles = [4, 2, [12, 39], [10, 37]]

After

derived = [[[12, 10, 22, 15], [12, 37, 49, 15], [39, 10, 29, 12], [39, 37, 2, 12]], [12, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S115

S117 · implies

Before

source roles = [4, 3, [12, 39], [11, 38]]

After

derived = [[[12, 11, 23, 16], [12, 38, 50, 16], [39, 11, 28, 1], [39, 38, 1, 1]], [1, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S116

S118 · implies

Before

source roles = [4, 4, [12, 39], [12, 39]]

After

derived = [[[12, 12, 24, 17], [12, 39, 51, 17], [39, 12, 27, 0], [39, 39, 0, 0]], [0, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S117

S119 · implies

Before

source roles = [4, 5, [12, 39], [13, 40]]

After

derived = [[[12, 13, 25, 18], [12, 40, 52, 18], [39, 13, 53, 19], [39, 40, 26, 19]], [18, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S118

S120 · implies

Before

source roles = [4, 6, [12, 39], [14, 41]]

After

derived = [[[12, 14, 26, 19], [12, 41, 53, 19], [39, 14, 52, 18], [39, 41, 25, 18]], [18, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S119

S121 · implies

Before

source roles = [4, 7, [12, 39], [15, 42]]

After

derived = [[[12, 15, 0, 0], [12, 42, 27, 0], [39, 15, 51, 17], [39, 42, 24, 17]], [0, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S120

S122 · implies

Before

source roles = [4, 8, [12, 39], [16, 43]]

After

derived = [[[12, 16, 1, 1], [12, 43, 28, 1], [39, 16, 50, 16], [39, 43, 23, 16]], [1, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S121

S123 · implies

Before

source roles = [4, 9, [12, 39], [17, 44]]

After

derived = [[[12, 17, 2, 12], [12, 44, 29, 12], [39, 17, 49, 15], [39, 44, 22, 15]], [12, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S122

S124 · implies

Before

source roles = [4, 10, [12, 39], [18, 45]]

After

derived = [[[12, 18, 3, 20], [12, 45, 30, 20], [39, 18, 48, 14], [39, 45, 21, 14]], [14, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S123

S125 · implies

Before

source roles = [4, 11, [12, 39], [19, 46]]

After

derived = [[[12, 19, 4, 21], [12, 46, 31, 21], [39, 19, 47, 13], [39, 46, 20, 13]], [13, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S124

S126 · implies

Before

source roles = [4, 12, [12, 39], [2, 29]]

After

derived = [[[12, 2, 14, 6], [12, 29, 41, 6], [39, 2, 37, 2], [39, 29, 10, 2]], [2, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S125

S127 · implies

Before

source roles = [4, 13, [12, 39], [20, 47]]

After

derived = [[[12, 20, 5, 22], [12, 47, 32, 22], [39, 20, 46, 11], [39, 47, 19, 11]], [11, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S126

S128 · implies

Before

source roles = [4, 14, [12, 39], [21, 48]]

After

derived = [[[12, 21, 6, 23], [12, 48, 33, 23], [39, 21, 45, 10], [39, 48, 18, 10]], [10, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S127

S129 · implies

Before

source roles = [4, 15, [12, 39], [22, 49]]

After

derived = [[[12, 22, 7, 24], [12, 49, 34, 24], [39, 22, 44, 9], [39, 49, 17, 9]], [9, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S128

S130 · implies

Before

source roles = [4, 16, [12, 39], [23, 50]]

After

derived = [[[12, 23, 8, 25], [12, 50, 35, 25], [39, 23, 43, 8], [39, 50, 16, 8]], [8, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S129

S131 · implies

Before

source roles = [4, 17, [12, 39], [24, 51]]

After

derived = [[[12, 24, 9, 26], [12, 51, 36, 26], [39, 24, 42, 7], [39, 51, 15, 7]], [7, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S130

S132 · implies

Before

source roles = [4, 18, [12, 39], [25, 52]]

After

derived = [[[12, 25, 10, 2], [12, 52, 37, 2], [39, 25, 41, 6], [39, 52, 14, 6]], [2, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S131

S133 · implies

Before

source roles = [4, 19, [12, 39], [26, 53]]

After

derived = [[[12, 26, 11, 3], [12, 53, 38, 3], [39, 26, 40, 5], [39, 53, 13, 5]], [3, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S132

S134 · implies

Before

source roles = [4, 20, [12, 39], [3, 30]]

After

derived = [[[12, 3, 15, 7], [12, 30, 42, 7], [39, 3, 36, 26], [39, 30, 9, 26]], [7, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S133

S135 · implies

Before

source roles = [4, 21, [12, 39], [4, 31]]

After

derived = [[[12, 4, 16, 8], [12, 31, 43, 8], [39, 4, 35, 25], [39, 31, 8, 25]], [8, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S134

S136 · implies

Before

source roles = [4, 22, [12, 39], [5, 32]]

After

derived = [[[12, 5, 17, 9], [12, 32, 44, 9], [39, 5, 34, 24], [39, 32, 7, 24]], [9, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S135

S137 · implies

Before

source roles = [4, 23, [12, 39], [6, 33]]

After

derived = [[[12, 6, 18, 10], [12, 33, 45, 10], [39, 6, 33, 23], [39, 33, 6, 23]], [10, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S136

S138 · implies

Before

source roles = [4, 24, [12, 39], [7, 34]]

After

derived = [[[12, 7, 19, 11], [12, 34, 46, 11], [39, 7, 32, 22], [39, 34, 5, 22]], [11, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S137

S139 · implies

Before

source roles = [4, 25, [12, 39], [8, 35]]

After

derived = [[[12, 8, 20, 13], [12, 35, 47, 13], [39, 8, 31, 21], [39, 35, 4, 21]], [13, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S138

S140 · implies

Before

source roles = [4, 26, [12, 39], [9, 36]]

After

derived = [[[12, 9, 21, 14], [12, 36, 48, 14], [39, 9, 30, 20], [39, 36, 3, 20]], [14, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S139

S141 · implies

Before

source roles = [5, 0, [13, 40], [0, 27]]

After

derived = [[[13, 0, 13, 5], [13, 27, 40, 5], [40, 0, 40, 5], [40, 27, 13, 5]], [5], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S140

S142 · implies

Before

source roles = [5, 1, [13, 40], [1, 28]]

After

derived = [[[13, 1, 14, 6], [13, 28, 41, 6], [40, 1, 39, 4], [40, 28, 12, 4]], [4, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S141

S143 · implies

Before

source roles = [5, 2, [13, 40], [10, 37]]

After

derived = [[[13, 10, 23, 16], [13, 37, 50, 16], [40, 10, 30, 20], [40, 37, 3, 20]], [16, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S142

S144 · implies

Before

source roles = [5, 3, [13, 40], [11, 38]]

After

derived = [[[13, 11, 24, 17], [13, 38, 51, 17], [40, 11, 29, 12], [40, 38, 2, 12]], [12, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S143

S145 · implies

Before

source roles = [5, 4, [13, 40], [12, 39]]

After

derived = [[[13, 12, 25, 18], [13, 39, 52, 18], [40, 12, 28, 1], [40, 39, 1, 1]], [1, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S144

S146 · implies

Before

source roles = [5, 5, [13, 40], [13, 40]]

After

derived = [[[13, 13, 26, 19], [13, 40, 53, 19], [40, 13, 27, 0], [40, 40, 0, 0]], [0, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S145

S147 · implies

Before

source roles = [5, 6, [13, 40], [14, 41]]

After

derived = [[[13, 14, 0, 0], [13, 41, 27, 0], [40, 14, 53, 19], [40, 41, 26, 19]], [0, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S146

S148 · implies

Before

source roles = [5, 7, [13, 40], [15, 42]]

After

derived = [[[13, 15, 1, 1], [13, 42, 28, 1], [40, 15, 52, 18], [40, 42, 25, 18]], [1, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S147

S149 · implies

Before

source roles = [5, 8, [13, 40], [16, 43]]

After

derived = [[[13, 16, 2, 12], [13, 43, 29, 12], [40, 16, 51, 17], [40, 43, 24, 17]], [12, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S148

S150 · implies

Before

source roles = [5, 9, [13, 40], [17, 44]]

After

derived = [[[13, 17, 3, 20], [13, 44, 30, 20], [40, 17, 50, 16], [40, 44, 23, 16]], [16, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S149

S151 · implies

Before

source roles = [5, 10, [13, 40], [18, 45]]

After

derived = [[[13, 18, 4, 21], [13, 45, 31, 21], [40, 18, 49, 15], [40, 45, 22, 15]], [15, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S150

S152 · implies

Before

source roles = [5, 11, [13, 40], [19, 46]]

After

derived = [[[13, 19, 5, 22], [13, 46, 32, 22], [40, 19, 48, 14], [40, 46, 21, 14]], [14, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S151

S153 · implies

Before

source roles = [5, 12, [13, 40], [2, 29]]

After

derived = [[[13, 2, 15, 7], [13, 29, 42, 7], [40, 2, 38, 3], [40, 29, 11, 3]], [3, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S152

S154 · implies

Before

source roles = [5, 13, [13, 40], [20, 47]]

After

derived = [[[13, 20, 6, 23], [13, 47, 33, 23], [40, 20, 47, 13], [40, 47, 20, 13]], [13, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S153

S155 · implies

Before

source roles = [5, 14, [13, 40], [21, 48]]

After

derived = [[[13, 21, 7, 24], [13, 48, 34, 24], [40, 21, 46, 11], [40, 48, 19, 11]], [11, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S154

S156 · implies

Before

source roles = [5, 15, [13, 40], [22, 49]]

After

derived = [[[13, 22, 8, 25], [13, 49, 35, 25], [40, 22, 45, 10], [40, 49, 18, 10]], [10, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S155

S157 · implies

Before

source roles = [5, 16, [13, 40], [23, 50]]

After

derived = [[[13, 23, 9, 26], [13, 50, 36, 26], [40, 23, 44, 9], [40, 50, 17, 9]], [9, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S156

S158 · implies

Before

source roles = [5, 17, [13, 40], [24, 51]]

After

derived = [[[13, 24, 10, 2], [13, 51, 37, 2], [40, 24, 43, 8], [40, 51, 16, 8]], [2, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S157

S159 · implies

Before

source roles = [5, 18, [13, 40], [25, 52]]

After

derived = [[[13, 25, 11, 3], [13, 52, 38, 3], [40, 25, 42, 7], [40, 52, 15, 7]], [3, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S158

S160 · implies

Before

source roles = [5, 19, [13, 40], [26, 53]]

After

derived = [[[13, 26, 12, 4], [13, 53, 39, 4], [40, 26, 41, 6], [40, 53, 14, 6]], [4, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S159

S161 · implies

Before

source roles = [5, 20, [13, 40], [3, 30]]

After

derived = [[[13, 3, 16, 8], [13, 30, 43, 8], [40, 3, 37, 2], [40, 30, 10, 2]], [2, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S160

S162 · implies

Before

source roles = [5, 21, [13, 40], [4, 31]]

After

derived = [[[13, 4, 17, 9], [13, 31, 44, 9], [40, 4, 36, 26], [40, 31, 9, 26]], [9, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S161

S163 · implies

Before

source roles = [5, 22, [13, 40], [5, 32]]

After

derived = [[[13, 5, 18, 10], [13, 32, 45, 10], [40, 5, 35, 25], [40, 32, 8, 25]], [10, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S162

S164 · implies

Before

source roles = [5, 23, [13, 40], [6, 33]]

After

derived = [[[13, 6, 19, 11], [13, 33, 46, 11], [40, 6, 34, 24], [40, 33, 7, 24]], [11, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S163

S165 · implies

Before

source roles = [5, 24, [13, 40], [7, 34]]

After

derived = [[[13, 7, 20, 13], [13, 34, 47, 13], [40, 7, 33, 23], [40, 34, 6, 23]], [13, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S164

S166 · implies

Before

source roles = [5, 25, [13, 40], [8, 35]]

After

derived = [[[13, 8, 21, 14], [13, 35, 48, 14], [40, 8, 32, 22], [40, 35, 5, 22]], [14, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S165

S167 · implies

Before

source roles = [5, 26, [13, 40], [9, 36]]

After

derived = [[[13, 9, 22, 15], [13, 36, 49, 15], [40, 9, 31, 21], [40, 36, 4, 21]], [15, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S166

S168 · implies

Before

source roles = [6, 0, [14, 41], [0, 27]]

After

derived = [[[14, 0, 14, 6], [14, 27, 41, 6], [41, 0, 41, 6], [41, 27, 14, 6]], [6], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S167

S169 · implies

Before

source roles = [6, 1, [14, 41], [1, 28]]

After

derived = [[[14, 1, 15, 7], [14, 28, 42, 7], [41, 1, 40, 5], [41, 28, 13, 5]], [5, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S168

S170 · implies

Before

source roles = [6, 2, [14, 41], [10, 37]]

After

derived = [[[14, 10, 24, 17], [14, 37, 51, 17], [41, 10, 31, 21], [41, 37, 4, 21]], [17, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S169

S171 · implies

Before

source roles = [6, 3, [14, 41], [11, 38]]

After

derived = [[[14, 11, 25, 18], [14, 38, 52, 18], [41, 11, 30, 20], [41, 38, 3, 20]], [18, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S170

S172 · implies

Before

source roles = [6, 4, [14, 41], [12, 39]]

After

derived = [[[14, 12, 26, 19], [14, 39, 53, 19], [41, 12, 29, 12], [41, 39, 2, 12]], [12, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S171

S173 · implies

Before

source roles = [6, 5, [14, 41], [13, 40]]

After

derived = [[[14, 13, 0, 0], [14, 40, 27, 0], [41, 13, 28, 1], [41, 40, 1, 1]], [0, 1], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S172

S174 · implies

Before

source roles = [6, 6, [14, 41], [14, 41]]

After

derived = [[[14, 14, 1, 1], [14, 41, 28, 1], [41, 14, 27, 0], [41, 41, 0, 0]], [0, 1], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S173

S175 · implies

Before

source roles = [6, 7, [14, 41], [15, 42]]

After

derived = [[[14, 15, 2, 12], [14, 42, 29, 12], [41, 15, 53, 19], [41, 42, 26, 19]], [12, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S174

S176 · implies

Before

source roles = [6, 8, [14, 41], [16, 43]]

After

derived = [[[14, 16, 3, 20], [14, 43, 30, 20], [41, 16, 52, 18], [41, 43, 25, 18]], [18, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S175

S177 · implies

Before

source roles = [6, 9, [14, 41], [17, 44]]

After

derived = [[[14, 17, 4, 21], [14, 44, 31, 21], [41, 17, 51, 17], [41, 44, 24, 17]], [17, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S176

S178 · implies

Before

source roles = [6, 10, [14, 41], [18, 45]]

After

derived = [[[14, 18, 5, 22], [14, 45, 32, 22], [41, 18, 50, 16], [41, 45, 23, 16]], [16, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S177

S179 · implies

Before

source roles = [6, 11, [14, 41], [19, 46]]

After

derived = [[[14, 19, 6, 23], [14, 46, 33, 23], [41, 19, 49, 15], [41, 46, 22, 15]], [15, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S178

S180 · implies

Before

source roles = [6, 12, [14, 41], [2, 29]]

After

derived = [[[14, 2, 16, 8], [14, 29, 43, 8], [41, 2, 39, 4], [41, 29, 12, 4]], [4, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S179

S181 · implies

Before

source roles = [6, 13, [14, 41], [20, 47]]

After

derived = [[[14, 20, 7, 24], [14, 47, 34, 24], [41, 20, 48, 14], [41, 47, 21, 14]], [14, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S180

S182 · implies

Before

source roles = [6, 14, [14, 41], [21, 48]]

After

derived = [[[14, 21, 8, 25], [14, 48, 35, 25], [41, 21, 47, 13], [41, 48, 20, 13]], [13, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S181

S183 · implies

Before

source roles = [6, 15, [14, 41], [22, 49]]

After

derived = [[[14, 22, 9, 26], [14, 49, 36, 26], [41, 22, 46, 11], [41, 49, 19, 11]], [11, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S182

S184 · implies

Before

source roles = [6, 16, [14, 41], [23, 50]]

After

derived = [[[14, 23, 10, 2], [14, 50, 37, 2], [41, 23, 45, 10], [41, 50, 18, 10]], [2, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S183

S185 · implies

Before

source roles = [6, 17, [14, 41], [24, 51]]

After

derived = [[[14, 24, 11, 3], [14, 51, 38, 3], [41, 24, 44, 9], [41, 51, 17, 9]], [3, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S184

S186 · implies

Before

source roles = [6, 18, [14, 41], [25, 52]]

After

derived = [[[14, 25, 12, 4], [14, 52, 39, 4], [41, 25, 43, 8], [41, 52, 16, 8]], [4, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S185

S187 · implies

Before

source roles = [6, 19, [14, 41], [26, 53]]

After

derived = [[[14, 26, 13, 5], [14, 53, 40, 5], [41, 26, 42, 7], [41, 53, 15, 7]], [5, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S186

S188 · implies

Before

source roles = [6, 20, [14, 41], [3, 30]]

After

derived = [[[14, 3, 17, 9], [14, 30, 44, 9], [41, 3, 38, 3], [41, 30, 11, 3]], [3, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S187

S189 · implies

Before

source roles = [6, 21, [14, 41], [4, 31]]

After

derived = [[[14, 4, 18, 10], [14, 31, 45, 10], [41, 4, 37, 2], [41, 31, 10, 2]], [2, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S188

S190 · implies

Before

source roles = [6, 22, [14, 41], [5, 32]]

After

derived = [[[14, 5, 19, 11], [14, 32, 46, 11], [41, 5, 36, 26], [41, 32, 9, 26]], [11, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S189

S191 · implies

Before

source roles = [6, 23, [14, 41], [6, 33]]

After

derived = [[[14, 6, 20, 13], [14, 33, 47, 13], [41, 6, 35, 25], [41, 33, 8, 25]], [13, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S190

S192 · implies

Before

source roles = [6, 24, [14, 41], [7, 34]]

After

derived = [[[14, 7, 21, 14], [14, 34, 48, 14], [41, 7, 34, 24], [41, 34, 7, 24]], [14, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S191

S193 · implies

Before

source roles = [6, 25, [14, 41], [8, 35]]

After

derived = [[[14, 8, 22, 15], [14, 35, 49, 15], [41, 8, 33, 23], [41, 35, 6, 23]], [15, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S192

S194 · implies

Before

source roles = [6, 26, [14, 41], [9, 36]]

After

derived = [[[14, 9, 23, 16], [14, 36, 50, 16], [41, 9, 32, 22], [41, 36, 5, 22]], [16, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S193

S195 · implies

Before

source roles = [7, 0, [15, 42], [0, 27]]

After

derived = [[[15, 0, 15, 7], [15, 27, 42, 7], [42, 0, 42, 7], [42, 27, 15, 7]], [7], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S194

S196 · implies

Before

source roles = [7, 1, [15, 42], [1, 28]]

After

derived = [[[15, 1, 16, 8], [15, 28, 43, 8], [42, 1, 41, 6], [42, 28, 14, 6]], [6, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S195

S197 · implies

Before

source roles = [7, 2, [15, 42], [10, 37]]

After

derived = [[[15, 10, 25, 18], [15, 37, 52, 18], [42, 10, 32, 22], [42, 37, 5, 22]], [18, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S196

S198 · implies

Before

source roles = [7, 3, [15, 42], [11, 38]]

After

derived = [[[15, 11, 26, 19], [15, 38, 53, 19], [42, 11, 31, 21], [42, 38, 4, 21]], [19, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S197

S199 · implies

Before

source roles = [7, 4, [15, 42], [12, 39]]

After

derived = [[[15, 12, 0, 0], [15, 39, 27, 0], [42, 12, 30, 20], [42, 39, 3, 20]], [0, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S198

S200 · implies

Before

source roles = [7, 5, [15, 42], [13, 40]]

After

derived = [[[15, 13, 1, 1], [15, 40, 28, 1], [42, 13, 29, 12], [42, 40, 2, 12]], [1, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S199

S201 · implies

Before

source roles = [7, 6, [15, 42], [14, 41]]

After

derived = [[[15, 14, 2, 12], [15, 41, 29, 12], [42, 14, 28, 1], [42, 41, 1, 1]], [1, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S200

S202 · implies

Before

source roles = [7, 7, [15, 42], [15, 42]]

After

derived = [[[15, 15, 3, 20], [15, 42, 30, 20], [42, 15, 27, 0], [42, 42, 0, 0]], [0, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S201

S203 · implies

Before

source roles = [7, 8, [15, 42], [16, 43]]

After

derived = [[[15, 16, 4, 21], [15, 43, 31, 21], [42, 16, 53, 19], [42, 43, 26, 19]], [19, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S202

S204 · implies

Before

source roles = [7, 9, [15, 42], [17, 44]]

After

derived = [[[15, 17, 5, 22], [15, 44, 32, 22], [42, 17, 52, 18], [42, 44, 25, 18]], [18, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S203

S205 · implies

Before

source roles = [7, 10, [15, 42], [18, 45]]

After

derived = [[[15, 18, 6, 23], [15, 45, 33, 23], [42, 18, 51, 17], [42, 45, 24, 17]], [17, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S204

S206 · implies

Before

source roles = [7, 11, [15, 42], [19, 46]]

After

derived = [[[15, 19, 7, 24], [15, 46, 34, 24], [42, 19, 50, 16], [42, 46, 23, 16]], [16, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S205

S207 · implies

Before

source roles = [7, 12, [15, 42], [2, 29]]

After

derived = [[[15, 2, 17, 9], [15, 29, 44, 9], [42, 2, 40, 5], [42, 29, 13, 5]], [5, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S206

S208 · implies

Before

source roles = [7, 13, [15, 42], [20, 47]]

After

derived = [[[15, 20, 8, 25], [15, 47, 35, 25], [42, 20, 49, 15], [42, 47, 22, 15]], [15, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S207

S209 · implies

Before

source roles = [7, 14, [15, 42], [21, 48]]

After

derived = [[[15, 21, 9, 26], [15, 48, 36, 26], [42, 21, 48, 14], [42, 48, 21, 14]], [14, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S208

S210 · implies

Before

source roles = [7, 15, [15, 42], [22, 49]]

After

derived = [[[15, 22, 10, 2], [15, 49, 37, 2], [42, 22, 47, 13], [42, 49, 20, 13]], [2, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S209

S211 · implies

Before

source roles = [7, 16, [15, 42], [23, 50]]

After

derived = [[[15, 23, 11, 3], [15, 50, 38, 3], [42, 23, 46, 11], [42, 50, 19, 11]], [3, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S210

S212 · implies

Before

source roles = [7, 17, [15, 42], [24, 51]]

After

derived = [[[15, 24, 12, 4], [15, 51, 39, 4], [42, 24, 45, 10], [42, 51, 18, 10]], [4, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S211

S213 · implies

Before

source roles = [7, 18, [15, 42], [25, 52]]

After

derived = [[[15, 25, 13, 5], [15, 52, 40, 5], [42, 25, 44, 9], [42, 52, 17, 9]], [5, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S212

S214 · implies

Before

source roles = [7, 19, [15, 42], [26, 53]]

After

derived = [[[15, 26, 14, 6], [15, 53, 41, 6], [42, 26, 43, 8], [42, 53, 16, 8]], [6, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S213

S215 · implies

Before

source roles = [7, 20, [15, 42], [3, 30]]

After

derived = [[[15, 3, 18, 10], [15, 30, 45, 10], [42, 3, 39, 4], [42, 30, 12, 4]], [4, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S214

S216 · implies

Before

source roles = [7, 21, [15, 42], [4, 31]]

After

derived = [[[15, 4, 19, 11], [15, 31, 46, 11], [42, 4, 38, 3], [42, 31, 11, 3]], [3, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S215

S217 · implies

Before

source roles = [7, 22, [15, 42], [5, 32]]

After

derived = [[[15, 5, 20, 13], [15, 32, 47, 13], [42, 5, 37, 2], [42, 32, 10, 2]], [2, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S216

S218 · implies

Before

source roles = [7, 23, [15, 42], [6, 33]]

After

derived = [[[15, 6, 21, 14], [15, 33, 48, 14], [42, 6, 36, 26], [42, 33, 9, 26]], [14, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S217

S219 · implies

Before

source roles = [7, 24, [15, 42], [7, 34]]

After

derived = [[[15, 7, 22, 15], [15, 34, 49, 15], [42, 7, 35, 25], [42, 34, 8, 25]], [15, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S218

S220 · implies

Before

source roles = [7, 25, [15, 42], [8, 35]]

After

derived = [[[15, 8, 23, 16], [15, 35, 50, 16], [42, 8, 34, 24], [42, 35, 7, 24]], [16, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S219

S221 · implies

Before

source roles = [7, 26, [15, 42], [9, 36]]

After

derived = [[[15, 9, 24, 17], [15, 36, 51, 17], [42, 9, 33, 23], [42, 36, 6, 23]], [17, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S220

S222 · implies

Before

source roles = [8, 0, [16, 43], [0, 27]]

After

derived = [[[16, 0, 16, 8], [16, 27, 43, 8], [43, 0, 43, 8], [43, 27, 16, 8]], [8], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S221

S223 · implies

Before

source roles = [8, 1, [16, 43], [1, 28]]

After

derived = [[[16, 1, 17, 9], [16, 28, 44, 9], [43, 1, 42, 7], [43, 28, 15, 7]], [7, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S222

S224 · implies

Before

source roles = [8, 2, [16, 43], [10, 37]]

After

derived = [[[16, 10, 26, 19], [16, 37, 53, 19], [43, 10, 33, 23], [43, 37, 6, 23]], [19, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S223

S225 · implies

Before

source roles = [8, 3, [16, 43], [11, 38]]

After

derived = [[[16, 11, 0, 0], [16, 38, 27, 0], [43, 11, 32, 22], [43, 38, 5, 22]], [0, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S224

S226 · implies

Before

source roles = [8, 4, [16, 43], [12, 39]]

After

derived = [[[16, 12, 1, 1], [16, 39, 28, 1], [43, 12, 31, 21], [43, 39, 4, 21]], [1, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S225

S227 · implies

Before

source roles = [8, 5, [16, 43], [13, 40]]

After

derived = [[[16, 13, 2, 12], [16, 40, 29, 12], [43, 13, 30, 20], [43, 40, 3, 20]], [12, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S226

S228 · implies

Before

source roles = [8, 6, [16, 43], [14, 41]]

After

derived = [[[16, 14, 3, 20], [16, 41, 30, 20], [43, 14, 29, 12], [43, 41, 2, 12]], [12, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S227

S229 · implies

Before

source roles = [8, 7, [16, 43], [15, 42]]

After

derived = [[[16, 15, 4, 21], [16, 42, 31, 21], [43, 15, 28, 1], [43, 42, 1, 1]], [1, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S228

S230 · implies

Before

source roles = [8, 8, [16, 43], [16, 43]]

After

derived = [[[16, 16, 5, 22], [16, 43, 32, 22], [43, 16, 27, 0], [43, 43, 0, 0]], [0, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S229

S231 · implies

Before

source roles = [8, 9, [16, 43], [17, 44]]

After

derived = [[[16, 17, 6, 23], [16, 44, 33, 23], [43, 17, 53, 19], [43, 44, 26, 19]], [19, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S230

S232 · implies

Before

source roles = [8, 10, [16, 43], [18, 45]]

After

derived = [[[16, 18, 7, 24], [16, 45, 34, 24], [43, 18, 52, 18], [43, 45, 25, 18]], [18, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S231

S233 · implies

Before

source roles = [8, 11, [16, 43], [19, 46]]

After

derived = [[[16, 19, 8, 25], [16, 46, 35, 25], [43, 19, 51, 17], [43, 46, 24, 17]], [17, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S232

S234 · implies

Before

source roles = [8, 12, [16, 43], [2, 29]]

After

derived = [[[16, 2, 18, 10], [16, 29, 45, 10], [43, 2, 41, 6], [43, 29, 14, 6]], [6, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S233

S235 · implies

Before

source roles = [8, 13, [16, 43], [20, 47]]

After

derived = [[[16, 20, 9, 26], [16, 47, 36, 26], [43, 20, 50, 16], [43, 47, 23, 16]], [16, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S234

S236 · implies

Before

source roles = [8, 14, [16, 43], [21, 48]]

After

derived = [[[16, 21, 10, 2], [16, 48, 37, 2], [43, 21, 49, 15], [43, 48, 22, 15]], [2, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S235

S237 · implies

Before

source roles = [8, 15, [16, 43], [22, 49]]

After

derived = [[[16, 22, 11, 3], [16, 49, 38, 3], [43, 22, 48, 14], [43, 49, 21, 14]], [3, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S236

S238 · implies

Before

source roles = [8, 16, [16, 43], [23, 50]]

After

derived = [[[16, 23, 12, 4], [16, 50, 39, 4], [43, 23, 47, 13], [43, 50, 20, 13]], [4, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S237

S239 · implies

Before

source roles = [8, 17, [16, 43], [24, 51]]

After

derived = [[[16, 24, 13, 5], [16, 51, 40, 5], [43, 24, 46, 11], [43, 51, 19, 11]], [5, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S238

S240 · implies

Before

source roles = [8, 18, [16, 43], [25, 52]]

After

derived = [[[16, 25, 14, 6], [16, 52, 41, 6], [43, 25, 45, 10], [43, 52, 18, 10]], [6, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S239

S241 · implies

Before

source roles = [8, 19, [16, 43], [26, 53]]

After

derived = [[[16, 26, 15, 7], [16, 53, 42, 7], [43, 26, 44, 9], [43, 53, 17, 9]], [7, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S240

S242 · implies

Before

source roles = [8, 20, [16, 43], [3, 30]]

After

derived = [[[16, 3, 19, 11], [16, 30, 46, 11], [43, 3, 40, 5], [43, 30, 13, 5]], [5, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S241

S243 · implies

Before

source roles = [8, 21, [16, 43], [4, 31]]

After

derived = [[[16, 4, 20, 13], [16, 31, 47, 13], [43, 4, 39, 4], [43, 31, 12, 4]], [4, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S242

S244 · implies

Before

source roles = [8, 22, [16, 43], [5, 32]]

After

derived = [[[16, 5, 21, 14], [16, 32, 48, 14], [43, 5, 38, 3], [43, 32, 11, 3]], [3, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S243

S245 · implies

Before

source roles = [8, 23, [16, 43], [6, 33]]

After

derived = [[[16, 6, 22, 15], [16, 33, 49, 15], [43, 6, 37, 2], [43, 33, 10, 2]], [2, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S244

S246 · implies

Before

source roles = [8, 24, [16, 43], [7, 34]]

After

derived = [[[16, 7, 23, 16], [16, 34, 50, 16], [43, 7, 36, 26], [43, 34, 9, 26]], [16, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S245

S247 · implies

Before

source roles = [8, 25, [16, 43], [8, 35]]

After

derived = [[[16, 8, 24, 17], [16, 35, 51, 17], [43, 8, 35, 25], [43, 35, 8, 25]], [17, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S246

S248 · implies

Before

source roles = [8, 26, [16, 43], [9, 36]]

After

derived = [[[16, 9, 25, 18], [16, 36, 52, 18], [43, 9, 34, 24], [43, 36, 7, 24]], [18, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S247

S249 · implies

Before

source roles = [9, 0, [17, 44], [0, 27]]

After

derived = [[[17, 0, 17, 9], [17, 27, 44, 9], [44, 0, 44, 9], [44, 27, 17, 9]], [9], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S248

S250 · implies

Before

source roles = [9, 1, [17, 44], [1, 28]]

After

derived = [[[17, 1, 18, 10], [17, 28, 45, 10], [44, 1, 43, 8], [44, 28, 16, 8]], [8, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S249

S251 · implies

Before

source roles = [9, 2, [17, 44], [10, 37]]

After

derived = [[[17, 10, 0, 0], [17, 37, 27, 0], [44, 10, 34, 24], [44, 37, 7, 24]], [0, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S250

S252 · implies

Before

source roles = [9, 3, [17, 44], [11, 38]]

After

derived = [[[17, 11, 1, 1], [17, 38, 28, 1], [44, 11, 33, 23], [44, 38, 6, 23]], [1, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S251

S253 · implies

Before

source roles = [9, 4, [17, 44], [12, 39]]

After

derived = [[[17, 12, 2, 12], [17, 39, 29, 12], [44, 12, 32, 22], [44, 39, 5, 22]], [12, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S252

S254 · implies

Before

source roles = [9, 5, [17, 44], [13, 40]]

After

derived = [[[17, 13, 3, 20], [17, 40, 30, 20], [44, 13, 31, 21], [44, 40, 4, 21]], [20, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S253

S255 · implies

Before

source roles = [9, 6, [17, 44], [14, 41]]

After

derived = [[[17, 14, 4, 21], [17, 41, 31, 21], [44, 14, 30, 20], [44, 41, 3, 20]], [20, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S254

S256 · implies

Before

source roles = [9, 7, [17, 44], [15, 42]]

After

derived = [[[17, 15, 5, 22], [17, 42, 32, 22], [44, 15, 29, 12], [44, 42, 2, 12]], [12, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S255

S257 · implies

Before

source roles = [9, 8, [17, 44], [16, 43]]

After

derived = [[[17, 16, 6, 23], [17, 43, 33, 23], [44, 16, 28, 1], [44, 43, 1, 1]], [1, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S256

S258 · implies

Before

source roles = [9, 9, [17, 44], [17, 44]]

After

derived = [[[17, 17, 7, 24], [17, 44, 34, 24], [44, 17, 27, 0], [44, 44, 0, 0]], [0, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S257

S259 · implies

Before

source roles = [9, 10, [17, 44], [18, 45]]

After

derived = [[[17, 18, 8, 25], [17, 45, 35, 25], [44, 18, 53, 19], [44, 45, 26, 19]], [19, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S258

S260 · implies

Before

source roles = [9, 11, [17, 44], [19, 46]]

After

derived = [[[17, 19, 9, 26], [17, 46, 36, 26], [44, 19, 52, 18], [44, 46, 25, 18]], [18, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S259

S261 · implies

Before

source roles = [9, 12, [17, 44], [2, 29]]

After

derived = [[[17, 2, 19, 11], [17, 29, 46, 11], [44, 2, 42, 7], [44, 29, 15, 7]], [7, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S260

S262 · implies

Before

source roles = [9, 13, [17, 44], [20, 47]]

After

derived = [[[17, 20, 10, 2], [17, 47, 37, 2], [44, 20, 51, 17], [44, 47, 24, 17]], [2, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S261

S263 · implies

Before

source roles = [9, 14, [17, 44], [21, 48]]

After

derived = [[[17, 21, 11, 3], [17, 48, 38, 3], [44, 21, 50, 16], [44, 48, 23, 16]], [3, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S262

S264 · implies

Before

source roles = [9, 15, [17, 44], [22, 49]]

After

derived = [[[17, 22, 12, 4], [17, 49, 39, 4], [44, 22, 49, 15], [44, 49, 22, 15]], [4, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S263

S265 · implies

Before

source roles = [9, 16, [17, 44], [23, 50]]

After

derived = [[[17, 23, 13, 5], [17, 50, 40, 5], [44, 23, 48, 14], [44, 50, 21, 14]], [5, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S264

S266 · implies

Before

source roles = [9, 17, [17, 44], [24, 51]]

After

derived = [[[17, 24, 14, 6], [17, 51, 41, 6], [44, 24, 47, 13], [44, 51, 20, 13]], [6, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S265

S267 · implies

Before

source roles = [9, 18, [17, 44], [25, 52]]

After

derived = [[[17, 25, 15, 7], [17, 52, 42, 7], [44, 25, 46, 11], [44, 52, 19, 11]], [7, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S266

S268 · implies

Before

source roles = [9, 19, [17, 44], [26, 53]]

After

derived = [[[17, 26, 16, 8], [17, 53, 43, 8], [44, 26, 45, 10], [44, 53, 18, 10]], [8, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S267

S269 · implies

Before

source roles = [9, 20, [17, 44], [3, 30]]

After

derived = [[[17, 3, 20, 13], [17, 30, 47, 13], [44, 3, 41, 6], [44, 30, 14, 6]], [6, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S268

S270 · implies

Before

source roles = [9, 21, [17, 44], [4, 31]]

After

derived = [[[17, 4, 21, 14], [17, 31, 48, 14], [44, 4, 40, 5], [44, 31, 13, 5]], [5, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S269

S271 · implies

Before

source roles = [9, 22, [17, 44], [5, 32]]

After

derived = [[[17, 5, 22, 15], [17, 32, 49, 15], [44, 5, 39, 4], [44, 32, 12, 4]], [4, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S270

S272 · implies

Before

source roles = [9, 23, [17, 44], [6, 33]]

After

derived = [[[17, 6, 23, 16], [17, 33, 50, 16], [44, 6, 38, 3], [44, 33, 11, 3]], [3, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S271

S273 · implies

Before

source roles = [9, 24, [17, 44], [7, 34]]

After

derived = [[[17, 7, 24, 17], [17, 34, 51, 17], [44, 7, 37, 2], [44, 34, 10, 2]], [2, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S272

S274 · implies

Before

source roles = [9, 25, [17, 44], [8, 35]]

After

derived = [[[17, 8, 25, 18], [17, 35, 52, 18], [44, 8, 36, 26], [44, 35, 9, 26]], [18, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S273

S275 · implies

Before

source roles = [9, 26, [17, 44], [9, 36]]

After

derived = [[[17, 9, 26, 19], [17, 36, 53, 19], [44, 9, 35, 25], [44, 36, 8, 25]], [19, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S274

S276 · implies

Before

source roles = [10, 0, [18, 45], [0, 27]]

After

derived = [[[18, 0, 18, 10], [18, 27, 45, 10], [45, 0, 45, 10], [45, 27, 18, 10]], [10], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S275

S277 · implies

Before

source roles = [10, 1, [18, 45], [1, 28]]

After

derived = [[[18, 1, 19, 11], [18, 28, 46, 11], [45, 1, 44, 9], [45, 28, 17, 9]], [9, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S276

S278 · implies

Before

source roles = [10, 2, [18, 45], [10, 37]]

After

derived = [[[18, 10, 1, 1], [18, 37, 28, 1], [45, 10, 35, 25], [45, 37, 8, 25]], [1, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S277

S279 · implies

Before

source roles = [10, 3, [18, 45], [11, 38]]

After

derived = [[[18, 11, 2, 12], [18, 38, 29, 12], [45, 11, 34, 24], [45, 38, 7, 24]], [12, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S278

S280 · implies

Before

source roles = [10, 4, [18, 45], [12, 39]]

After

derived = [[[18, 12, 3, 20], [18, 39, 30, 20], [45, 12, 33, 23], [45, 39, 6, 23]], [20, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S279

S281 · implies

Before

source roles = [10, 5, [18, 45], [13, 40]]

After

derived = [[[18, 13, 4, 21], [18, 40, 31, 21], [45, 13, 32, 22], [45, 40, 5, 22]], [21, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S280

S282 · implies

Before

source roles = [10, 6, [18, 45], [14, 41]]

After

derived = [[[18, 14, 5, 22], [18, 41, 32, 22], [45, 14, 31, 21], [45, 41, 4, 21]], [21, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S281

S283 · implies

Before

source roles = [10, 7, [18, 45], [15, 42]]

After

derived = [[[18, 15, 6, 23], [18, 42, 33, 23], [45, 15, 30, 20], [45, 42, 3, 20]], [20, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S282

S284 · implies

Before

source roles = [10, 8, [18, 45], [16, 43]]

After

derived = [[[18, 16, 7, 24], [18, 43, 34, 24], [45, 16, 29, 12], [45, 43, 2, 12]], [12, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S283

S285 · implies

Before

source roles = [10, 9, [18, 45], [17, 44]]

After

derived = [[[18, 17, 8, 25], [18, 44, 35, 25], [45, 17, 28, 1], [45, 44, 1, 1]], [1, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S284

S286 · implies

Before

source roles = [10, 10, [18, 45], [18, 45]]

After

derived = [[[18, 18, 9, 26], [18, 45, 36, 26], [45, 18, 27, 0], [45, 45, 0, 0]], [0, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S285

S287 · implies

Before

source roles = [10, 11, [18, 45], [19, 46]]

After

derived = [[[18, 19, 10, 2], [18, 46, 37, 2], [45, 19, 53, 19], [45, 46, 26, 19]], [2, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S286

S288 · implies

Before

source roles = [10, 12, [18, 45], [2, 29]]

After

derived = [[[18, 2, 20, 13], [18, 29, 47, 13], [45, 2, 43, 8], [45, 29, 16, 8]], [8, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S287

S289 · implies

Before

source roles = [10, 13, [18, 45], [20, 47]]

After

derived = [[[18, 20, 11, 3], [18, 47, 38, 3], [45, 20, 52, 18], [45, 47, 25, 18]], [3, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S288

S290 · implies

Before

source roles = [10, 14, [18, 45], [21, 48]]

After

derived = [[[18, 21, 12, 4], [18, 48, 39, 4], [45, 21, 51, 17], [45, 48, 24, 17]], [4, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S289

S291 · implies

Before

source roles = [10, 15, [18, 45], [22, 49]]

After

derived = [[[18, 22, 13, 5], [18, 49, 40, 5], [45, 22, 50, 16], [45, 49, 23, 16]], [5, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S290

S292 · implies

Before

source roles = [10, 16, [18, 45], [23, 50]]

After

derived = [[[18, 23, 14, 6], [18, 50, 41, 6], [45, 23, 49, 15], [45, 50, 22, 15]], [6, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S291

S293 · implies

Before

source roles = [10, 17, [18, 45], [24, 51]]

After

derived = [[[18, 24, 15, 7], [18, 51, 42, 7], [45, 24, 48, 14], [45, 51, 21, 14]], [7, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S292

S294 · implies

Before

source roles = [10, 18, [18, 45], [25, 52]]

After

derived = [[[18, 25, 16, 8], [18, 52, 43, 8], [45, 25, 47, 13], [45, 52, 20, 13]], [8, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S293

S295 · implies

Before

source roles = [10, 19, [18, 45], [26, 53]]

After

derived = [[[18, 26, 17, 9], [18, 53, 44, 9], [45, 26, 46, 11], [45, 53, 19, 11]], [9, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S294

S296 · implies

Before

source roles = [10, 20, [18, 45], [3, 30]]

After

derived = [[[18, 3, 21, 14], [18, 30, 48, 14], [45, 3, 42, 7], [45, 30, 15, 7]], [7, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S295

S297 · implies

Before

source roles = [10, 21, [18, 45], [4, 31]]

After

derived = [[[18, 4, 22, 15], [18, 31, 49, 15], [45, 4, 41, 6], [45, 31, 14, 6]], [6, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S296

S298 · implies

Before

source roles = [10, 22, [18, 45], [5, 32]]

After

derived = [[[18, 5, 23, 16], [18, 32, 50, 16], [45, 5, 40, 5], [45, 32, 13, 5]], [5, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S297

S299 · implies

Before

source roles = [10, 23, [18, 45], [6, 33]]

After

derived = [[[18, 6, 24, 17], [18, 33, 51, 17], [45, 6, 39, 4], [45, 33, 12, 4]], [4, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S298

S300 · implies

Before

source roles = [10, 24, [18, 45], [7, 34]]

After

derived = [[[18, 7, 25, 18], [18, 34, 52, 18], [45, 7, 38, 3], [45, 34, 11, 3]], [3, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S299

S301 · implies

Before

source roles = [10, 25, [18, 45], [8, 35]]

After

derived = [[[18, 8, 26, 19], [18, 35, 53, 19], [45, 8, 37, 2], [45, 35, 10, 2]], [2, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S300

S302 · implies

Before

source roles = [10, 26, [18, 45], [9, 36]]

After

derived = [[[18, 9, 0, 0], [18, 36, 27, 0], [45, 9, 36, 26], [45, 36, 9, 26]], [0, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S301

S303 · implies

Before

source roles = [11, 0, [19, 46], [0, 27]]

After

derived = [[[19, 0, 19, 11], [19, 27, 46, 11], [46, 0, 46, 11], [46, 27, 19, 11]], [11], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S302

S304 · implies

Before

source roles = [11, 1, [19, 46], [1, 28]]

After

derived = [[[19, 1, 20, 13], [19, 28, 47, 13], [46, 1, 45, 10], [46, 28, 18, 10]], [10, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S303

S305 · implies

Before

source roles = [11, 2, [19, 46], [10, 37]]

After

derived = [[[19, 10, 2, 12], [19, 37, 29, 12], [46, 10, 36, 26], [46, 37, 9, 26]], [12, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S304

S306 · implies

Before

source roles = [11, 3, [19, 46], [11, 38]]

After

derived = [[[19, 11, 3, 20], [19, 38, 30, 20], [46, 11, 35, 25], [46, 38, 8, 25]], [20, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S305

S307 · implies

Before

source roles = [11, 4, [19, 46], [12, 39]]

After

derived = [[[19, 12, 4, 21], [19, 39, 31, 21], [46, 12, 34, 24], [46, 39, 7, 24]], [21, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S306

S308 · implies

Before

source roles = [11, 5, [19, 46], [13, 40]]

After

derived = [[[19, 13, 5, 22], [19, 40, 32, 22], [46, 13, 33, 23], [46, 40, 6, 23]], [22, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S307

S309 · implies

Before

source roles = [11, 6, [19, 46], [14, 41]]

After

derived = [[[19, 14, 6, 23], [19, 41, 33, 23], [46, 14, 32, 22], [46, 41, 5, 22]], [22, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S308

S310 · implies

Before

source roles = [11, 7, [19, 46], [15, 42]]

After

derived = [[[19, 15, 7, 24], [19, 42, 34, 24], [46, 15, 31, 21], [46, 42, 4, 21]], [21, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S309

S311 · implies

Before

source roles = [11, 8, [19, 46], [16, 43]]

After

derived = [[[19, 16, 8, 25], [19, 43, 35, 25], [46, 16, 30, 20], [46, 43, 3, 20]], [20, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S310

S312 · implies

Before

source roles = [11, 9, [19, 46], [17, 44]]

After

derived = [[[19, 17, 9, 26], [19, 44, 36, 26], [46, 17, 29, 12], [46, 44, 2, 12]], [12, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S311

S313 · implies

Before

source roles = [11, 10, [19, 46], [18, 45]]

After

derived = [[[19, 18, 10, 2], [19, 45, 37, 2], [46, 18, 28, 1], [46, 45, 1, 1]], [1, 2], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S312

S314 · implies

Before

source roles = [11, 11, [19, 46], [19, 46]]

After

derived = [[[19, 19, 11, 3], [19, 46, 38, 3], [46, 19, 27, 0], [46, 46, 0, 0]], [0, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S313

S315 · implies

Before

source roles = [11, 12, [19, 46], [2, 29]]

After

derived = [[[19, 2, 21, 14], [19, 29, 48, 14], [46, 2, 44, 9], [46, 29, 17, 9]], [9, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S314

S316 · implies

Before

source roles = [11, 13, [19, 46], [20, 47]]

After

derived = [[[19, 20, 12, 4], [19, 47, 39, 4], [46, 20, 53, 19], [46, 47, 26, 19]], [4, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S315

S317 · implies

Before

source roles = [11, 14, [19, 46], [21, 48]]

After

derived = [[[19, 21, 13, 5], [19, 48, 40, 5], [46, 21, 52, 18], [46, 48, 25, 18]], [5, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S316

S318 · implies

Before

source roles = [11, 15, [19, 46], [22, 49]]

After

derived = [[[19, 22, 14, 6], [19, 49, 41, 6], [46, 22, 51, 17], [46, 49, 24, 17]], [6, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S317

S319 · implies

Before

source roles = [11, 16, [19, 46], [23, 50]]

After

derived = [[[19, 23, 15, 7], [19, 50, 42, 7], [46, 23, 50, 16], [46, 50, 23, 16]], [7, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S318

S320 · implies

Before

source roles = [11, 17, [19, 46], [24, 51]]

After

derived = [[[19, 24, 16, 8], [19, 51, 43, 8], [46, 24, 49, 15], [46, 51, 22, 15]], [8, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S319

S321 · implies

Before

source roles = [11, 18, [19, 46], [25, 52]]

After

derived = [[[19, 25, 17, 9], [19, 52, 44, 9], [46, 25, 48, 14], [46, 52, 21, 14]], [9, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S320

S322 · implies

Before

source roles = [11, 19, [19, 46], [26, 53]]

After

derived = [[[19, 26, 18, 10], [19, 53, 45, 10], [46, 26, 47, 13], [46, 53, 20, 13]], [10, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S321

S323 · implies

Before

source roles = [11, 20, [19, 46], [3, 30]]

After

derived = [[[19, 3, 22, 15], [19, 30, 49, 15], [46, 3, 43, 8], [46, 30, 16, 8]], [8, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S322

S324 · implies

Before

source roles = [11, 21, [19, 46], [4, 31]]

After

derived = [[[19, 4, 23, 16], [19, 31, 50, 16], [46, 4, 42, 7], [46, 31, 15, 7]], [7, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S323

S325 · implies

Before

source roles = [11, 22, [19, 46], [5, 32]]

After

derived = [[[19, 5, 24, 17], [19, 32, 51, 17], [46, 5, 41, 6], [46, 32, 14, 6]], [6, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S324

S326 · implies

Before

source roles = [11, 23, [19, 46], [6, 33]]

After

derived = [[[19, 6, 25, 18], [19, 33, 52, 18], [46, 6, 40, 5], [46, 33, 13, 5]], [5, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S325

S327 · implies

Before

source roles = [11, 24, [19, 46], [7, 34]]

After

derived = [[[19, 7, 26, 19], [19, 34, 53, 19], [46, 7, 39, 4], [46, 34, 12, 4]], [4, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S326

S328 · implies

Before

source roles = [11, 25, [19, 46], [8, 35]]

After

derived = [[[19, 8, 0, 0], [19, 35, 27, 0], [46, 8, 38, 3], [46, 35, 11, 3]], [0, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S327

S329 · implies

Before

source roles = [11, 26, [19, 46], [9, 36]]

After

derived = [[[19, 9, 1, 1], [19, 36, 28, 1], [46, 9, 37, 2], [46, 36, 10, 2]], [1, 2], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S328

S330 · implies

Before

source roles = [12, 0, [2, 29], [0, 27]]

After

derived = [[[2, 0, 2, 12], [2, 27, 29, 12], [29, 0, 29, 12], [29, 27, 2, 12]], [12], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S329

S331 · implies

Before

source roles = [12, 1, [2, 29], [1, 28]]

After

derived = [[[2, 1, 3, 20], [2, 28, 30, 20], [29, 1, 28, 1], [29, 28, 1, 1]], [1, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S330

S332 · implies

Before

source roles = [12, 2, [2, 29], [10, 37]]

After

derived = [[[2, 10, 12, 4], [2, 37, 39, 4], [29, 10, 46, 11], [29, 37, 19, 11]], [4, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S331

S333 · implies

Before

source roles = [12, 3, [2, 29], [11, 38]]

After

derived = [[[2, 11, 13, 5], [2, 38, 40, 5], [29, 11, 45, 10], [29, 38, 18, 10]], [5, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S332

S334 · implies

Before

source roles = [12, 4, [2, 29], [12, 39]]

After

derived = [[[2, 12, 14, 6], [2, 39, 41, 6], [29, 12, 44, 9], [29, 39, 17, 9]], [6, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S333

S335 · implies

Before

source roles = [12, 5, [2, 29], [13, 40]]

After

derived = [[[2, 13, 15, 7], [2, 40, 42, 7], [29, 13, 43, 8], [29, 40, 16, 8]], [7, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S334

S336 · implies

Before

source roles = [12, 6, [2, 29], [14, 41]]

After

derived = [[[2, 14, 16, 8], [2, 41, 43, 8], [29, 14, 42, 7], [29, 41, 15, 7]], [7, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S335

S337 · implies

Before

source roles = [12, 7, [2, 29], [15, 42]]

After

derived = [[[2, 15, 17, 9], [2, 42, 44, 9], [29, 15, 41, 6], [29, 42, 14, 6]], [6, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S336

S338 · implies

Before

source roles = [12, 8, [2, 29], [16, 43]]

After

derived = [[[2, 16, 18, 10], [2, 43, 45, 10], [29, 16, 40, 5], [29, 43, 13, 5]], [5, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S337

S339 · implies

Before

source roles = [12, 9, [2, 29], [17, 44]]

After

derived = [[[2, 17, 19, 11], [2, 44, 46, 11], [29, 17, 39, 4], [29, 44, 12, 4]], [4, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S338

S340 · implies

Before

source roles = [12, 10, [2, 29], [18, 45]]

After

derived = [[[2, 18, 20, 13], [2, 45, 47, 13], [29, 18, 38, 3], [29, 45, 11, 3]], [3, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S339

S341 · implies

Before

source roles = [12, 11, [2, 29], [19, 46]]

After

derived = [[[2, 19, 21, 14], [2, 46, 48, 14], [29, 19, 37, 2], [29, 46, 10, 2]], [2, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S340

S342 · implies

Before

source roles = [12, 12, [2, 29], [2, 29]]

After

derived = [[[2, 2, 4, 21], [2, 29, 31, 21], [29, 2, 27, 0], [29, 29, 0, 0]], [0, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S341

S343 · implies

Before

source roles = [12, 13, [2, 29], [20, 47]]

After

derived = [[[2, 20, 22, 15], [2, 47, 49, 15], [29, 20, 36, 26], [29, 47, 9, 26]], [15, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S342

S344 · implies

Before

source roles = [12, 14, [2, 29], [21, 48]]

After

derived = [[[2, 21, 23, 16], [2, 48, 50, 16], [29, 21, 35, 25], [29, 48, 8, 25]], [16, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S343

S345 · implies

Before

source roles = [12, 15, [2, 29], [22, 49]]

After

derived = [[[2, 22, 24, 17], [2, 49, 51, 17], [29, 22, 34, 24], [29, 49, 7, 24]], [17, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S344

S346 · implies

Before

source roles = [12, 16, [2, 29], [23, 50]]

After

derived = [[[2, 23, 25, 18], [2, 50, 52, 18], [29, 23, 33, 23], [29, 50, 6, 23]], [18, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S345

S347 · implies

Before

source roles = [12, 17, [2, 29], [24, 51]]

After

derived = [[[2, 24, 26, 19], [2, 51, 53, 19], [29, 24, 32, 22], [29, 51, 5, 22]], [19, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S346

S348 · implies

Before

source roles = [12, 18, [2, 29], [25, 52]]

After

derived = [[[2, 25, 0, 0], [2, 52, 27, 0], [29, 25, 31, 21], [29, 52, 4, 21]], [0, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S347

S349 · implies

Before

source roles = [12, 19, [2, 29], [26, 53]]

After

derived = [[[2, 26, 1, 1], [2, 53, 28, 1], [29, 26, 30, 20], [29, 53, 3, 20]], [1, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S348

S350 · implies

Before

source roles = [12, 20, [2, 29], [3, 30]]

After

derived = [[[2, 3, 5, 22], [2, 30, 32, 22], [29, 3, 53, 19], [29, 30, 26, 19]], [19, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S349

S351 · implies

Before

source roles = [12, 21, [2, 29], [4, 31]]

After

derived = [[[2, 4, 6, 23], [2, 31, 33, 23], [29, 4, 52, 18], [29, 31, 25, 18]], [18, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S350

S352 · implies

Before

source roles = [12, 22, [2, 29], [5, 32]]

After

derived = [[[2, 5, 7, 24], [2, 32, 34, 24], [29, 5, 51, 17], [29, 32, 24, 17]], [17, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S351

S353 · implies

Before

source roles = [12, 23, [2, 29], [6, 33]]

After

derived = [[[2, 6, 8, 25], [2, 33, 35, 25], [29, 6, 50, 16], [29, 33, 23, 16]], [16, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S352

S354 · implies

Before

source roles = [12, 24, [2, 29], [7, 34]]

After

derived = [[[2, 7, 9, 26], [2, 34, 36, 26], [29, 7, 49, 15], [29, 34, 22, 15]], [15, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S353

S355 · implies

Before

source roles = [12, 25, [2, 29], [8, 35]]

After

derived = [[[2, 8, 10, 2], [2, 35, 37, 2], [29, 8, 48, 14], [29, 35, 21, 14]], [2, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S354

S356 · implies

Before

source roles = [12, 26, [2, 29], [9, 36]]

After

derived = [[[2, 9, 11, 3], [2, 36, 38, 3], [29, 9, 47, 13], [29, 36, 20, 13]], [3, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S355

S357 · implies

Before

source roles = [13, 0, [20, 47], [0, 27]]

After

derived = [[[20, 0, 20, 13], [20, 27, 47, 13], [47, 0, 47, 13], [47, 27, 20, 13]], [13], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S356

S358 · implies

Before

source roles = [13, 1, [20, 47], [1, 28]]

After

derived = [[[20, 1, 21, 14], [20, 28, 48, 14], [47, 1, 46, 11], [47, 28, 19, 11]], [11, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S357

S359 · implies

Before

source roles = [13, 2, [20, 47], [10, 37]]

After

derived = [[[20, 10, 3, 20], [20, 37, 30, 20], [47, 10, 37, 2], [47, 37, 10, 2]], [2, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S358

S360 · implies

Before

source roles = [13, 3, [20, 47], [11, 38]]

After

derived = [[[20, 11, 4, 21], [20, 38, 31, 21], [47, 11, 36, 26], [47, 38, 9, 26]], [21, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S359

S361 · implies

Before

source roles = [13, 4, [20, 47], [12, 39]]

After

derived = [[[20, 12, 5, 22], [20, 39, 32, 22], [47, 12, 35, 25], [47, 39, 8, 25]], [22, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S360

S362 · implies

Before

source roles = [13, 5, [20, 47], [13, 40]]

After

derived = [[[20, 13, 6, 23], [20, 40, 33, 23], [47, 13, 34, 24], [47, 40, 7, 24]], [23, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S361

S363 · implies

Before

source roles = [13, 6, [20, 47], [14, 41]]

After

derived = [[[20, 14, 7, 24], [20, 41, 34, 24], [47, 14, 33, 23], [47, 41, 6, 23]], [23, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S362

S364 · implies

Before

source roles = [13, 7, [20, 47], [15, 42]]

After

derived = [[[20, 15, 8, 25], [20, 42, 35, 25], [47, 15, 32, 22], [47, 42, 5, 22]], [22, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S363

S365 · implies

Before

source roles = [13, 8, [20, 47], [16, 43]]

After

derived = [[[20, 16, 9, 26], [20, 43, 36, 26], [47, 16, 31, 21], [47, 43, 4, 21]], [21, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S364

S366 · implies

Before

source roles = [13, 9, [20, 47], [17, 44]]

After

derived = [[[20, 17, 10, 2], [20, 44, 37, 2], [47, 17, 30, 20], [47, 44, 3, 20]], [2, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S365

S367 · implies

Before

source roles = [13, 10, [20, 47], [18, 45]]

After

derived = [[[20, 18, 11, 3], [20, 45, 38, 3], [47, 18, 29, 12], [47, 45, 2, 12]], [3, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S366

S368 · implies

Before

source roles = [13, 11, [20, 47], [19, 46]]

After

derived = [[[20, 19, 12, 4], [20, 46, 39, 4], [47, 19, 28, 1], [47, 46, 1, 1]], [1, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S367

S369 · implies

Before

source roles = [13, 12, [20, 47], [2, 29]]

After

derived = [[[20, 2, 22, 15], [20, 29, 49, 15], [47, 2, 45, 10], [47, 29, 18, 10]], [10, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S368

S370 · implies

Before

source roles = [13, 13, [20, 47], [20, 47]]

After

derived = [[[20, 20, 13, 5], [20, 47, 40, 5], [47, 20, 27, 0], [47, 47, 0, 0]], [0, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S369

S371 · implies

Before

source roles = [13, 14, [20, 47], [21, 48]]

After

derived = [[[20, 21, 14, 6], [20, 48, 41, 6], [47, 21, 53, 19], [47, 48, 26, 19]], [6, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S370

S372 · implies

Before

source roles = [13, 15, [20, 47], [22, 49]]

After

derived = [[[20, 22, 15, 7], [20, 49, 42, 7], [47, 22, 52, 18], [47, 49, 25, 18]], [7, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S371

S373 · implies

Before

source roles = [13, 16, [20, 47], [23, 50]]

After

derived = [[[20, 23, 16, 8], [20, 50, 43, 8], [47, 23, 51, 17], [47, 50, 24, 17]], [8, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S372

S374 · implies

Before

source roles = [13, 17, [20, 47], [24, 51]]

After

derived = [[[20, 24, 17, 9], [20, 51, 44, 9], [47, 24, 50, 16], [47, 51, 23, 16]], [9, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S373

S375 · implies

Before

source roles = [13, 18, [20, 47], [25, 52]]

After

derived = [[[20, 25, 18, 10], [20, 52, 45, 10], [47, 25, 49, 15], [47, 52, 22, 15]], [10, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S374

S376 · implies

Before

source roles = [13, 19, [20, 47], [26, 53]]

After

derived = [[[20, 26, 19, 11], [20, 53, 46, 11], [47, 26, 48, 14], [47, 53, 21, 14]], [11, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S375

S377 · implies

Before

source roles = [13, 20, [20, 47], [3, 30]]

After

derived = [[[20, 3, 23, 16], [20, 30, 50, 16], [47, 3, 44, 9], [47, 30, 17, 9]], [9, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S376

S378 · implies

Before

source roles = [13, 21, [20, 47], [4, 31]]

After

derived = [[[20, 4, 24, 17], [20, 31, 51, 17], [47, 4, 43, 8], [47, 31, 16, 8]], [8, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S377

S379 · implies

Before

source roles = [13, 22, [20, 47], [5, 32]]

After

derived = [[[20, 5, 25, 18], [20, 32, 52, 18], [47, 5, 42, 7], [47, 32, 15, 7]], [7, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S378

S380 · implies

Before

source roles = [13, 23, [20, 47], [6, 33]]

After

derived = [[[20, 6, 26, 19], [20, 33, 53, 19], [47, 6, 41, 6], [47, 33, 14, 6]], [6, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S379

S381 · implies

Before

source roles = [13, 24, [20, 47], [7, 34]]

After

derived = [[[20, 7, 0, 0], [20, 34, 27, 0], [47, 7, 40, 5], [47, 34, 13, 5]], [0, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S380

S382 · implies

Before

source roles = [13, 25, [20, 47], [8, 35]]

After

derived = [[[20, 8, 1, 1], [20, 35, 28, 1], [47, 8, 39, 4], [47, 35, 12, 4]], [1, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S381

S383 · implies

Before

source roles = [13, 26, [20, 47], [9, 36]]

After

derived = [[[20, 9, 2, 12], [20, 36, 29, 12], [47, 9, 38, 3], [47, 36, 11, 3]], [3, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S382

S384 · implies

Before

source roles = [14, 0, [21, 48], [0, 27]]

After

derived = [[[21, 0, 21, 14], [21, 27, 48, 14], [48, 0, 48, 14], [48, 27, 21, 14]], [14], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S383

S385 · implies

Before

source roles = [14, 1, [21, 48], [1, 28]]

After

derived = [[[21, 1, 22, 15], [21, 28, 49, 15], [48, 1, 47, 13], [48, 28, 20, 13]], [13, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S384

S386 · implies

Before

source roles = [14, 2, [21, 48], [10, 37]]

After

derived = [[[21, 10, 4, 21], [21, 37, 31, 21], [48, 10, 38, 3], [48, 37, 11, 3]], [3, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S385

S387 · implies

Before

source roles = [14, 3, [21, 48], [11, 38]]

After

derived = [[[21, 11, 5, 22], [21, 38, 32, 22], [48, 11, 37, 2], [48, 38, 10, 2]], [2, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S386

S388 · implies

Before

source roles = [14, 4, [21, 48], [12, 39]]

After

derived = [[[21, 12, 6, 23], [21, 39, 33, 23], [48, 12, 36, 26], [48, 39, 9, 26]], [23, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S387

S389 · implies

Before

source roles = [14, 5, [21, 48], [13, 40]]

After

derived = [[[21, 13, 7, 24], [21, 40, 34, 24], [48, 13, 35, 25], [48, 40, 8, 25]], [24, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S388

S390 · implies

Before

source roles = [14, 6, [21, 48], [14, 41]]

After

derived = [[[21, 14, 8, 25], [21, 41, 35, 25], [48, 14, 34, 24], [48, 41, 7, 24]], [24, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S389

S391 · implies

Before

source roles = [14, 7, [21, 48], [15, 42]]

After

derived = [[[21, 15, 9, 26], [21, 42, 36, 26], [48, 15, 33, 23], [48, 42, 6, 23]], [23, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S390

S392 · implies

Before

source roles = [14, 8, [21, 48], [16, 43]]

After

derived = [[[21, 16, 10, 2], [21, 43, 37, 2], [48, 16, 32, 22], [48, 43, 5, 22]], [2, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S391

S393 · implies

Before

source roles = [14, 9, [21, 48], [17, 44]]

After

derived = [[[21, 17, 11, 3], [21, 44, 38, 3], [48, 17, 31, 21], [48, 44, 4, 21]], [3, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S392

S394 · implies

Before

source roles = [14, 10, [21, 48], [18, 45]]

After

derived = [[[21, 18, 12, 4], [21, 45, 39, 4], [48, 18, 30, 20], [48, 45, 3, 20]], [4, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S393

S395 · implies

Before

source roles = [14, 11, [21, 48], [19, 46]]

After

derived = [[[21, 19, 13, 5], [21, 46, 40, 5], [48, 19, 29, 12], [48, 46, 2, 12]], [5, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S394

S396 · implies

Before

source roles = [14, 12, [21, 48], [2, 29]]

After

derived = [[[21, 2, 23, 16], [21, 29, 50, 16], [48, 2, 46, 11], [48, 29, 19, 11]], [11, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S395

S397 · implies

Before

source roles = [14, 13, [21, 48], [20, 47]]

After

derived = [[[21, 20, 14, 6], [21, 47, 41, 6], [48, 20, 28, 1], [48, 47, 1, 1]], [1, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S396

S398 · implies

Before

source roles = [14, 14, [21, 48], [21, 48]]

After

derived = [[[21, 21, 15, 7], [21, 48, 42, 7], [48, 21, 27, 0], [48, 48, 0, 0]], [0, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S397

S399 · implies

Before

source roles = [14, 15, [21, 48], [22, 49]]

After

derived = [[[21, 22, 16, 8], [21, 49, 43, 8], [48, 22, 53, 19], [48, 49, 26, 19]], [8, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S398

S400 · implies

Before

source roles = [14, 16, [21, 48], [23, 50]]

After

derived = [[[21, 23, 17, 9], [21, 50, 44, 9], [48, 23, 52, 18], [48, 50, 25, 18]], [9, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S399

S401 · implies

Before

source roles = [14, 17, [21, 48], [24, 51]]

After

derived = [[[21, 24, 18, 10], [21, 51, 45, 10], [48, 24, 51, 17], [48, 51, 24, 17]], [10, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S400

S402 · implies

Before

source roles = [14, 18, [21, 48], [25, 52]]

After

derived = [[[21, 25, 19, 11], [21, 52, 46, 11], [48, 25, 50, 16], [48, 52, 23, 16]], [11, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S401

S403 · implies

Before

source roles = [14, 19, [21, 48], [26, 53]]

After

derived = [[[21, 26, 20, 13], [21, 53, 47, 13], [48, 26, 49, 15], [48, 53, 22, 15]], [13, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S402

S404 · implies

Before

source roles = [14, 20, [21, 48], [3, 30]]

After

derived = [[[21, 3, 24, 17], [21, 30, 51, 17], [48, 3, 45, 10], [48, 30, 18, 10]], [10, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S403

S405 · implies

Before

source roles = [14, 21, [21, 48], [4, 31]]

After

derived = [[[21, 4, 25, 18], [21, 31, 52, 18], [48, 4, 44, 9], [48, 31, 17, 9]], [9, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S404

S406 · implies

Before

source roles = [14, 22, [21, 48], [5, 32]]

After

derived = [[[21, 5, 26, 19], [21, 32, 53, 19], [48, 5, 43, 8], [48, 32, 16, 8]], [8, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S405

S407 · implies

Before

source roles = [14, 23, [21, 48], [6, 33]]

After

derived = [[[21, 6, 0, 0], [21, 33, 27, 0], [48, 6, 42, 7], [48, 33, 15, 7]], [0, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S406

S408 · implies

Before

source roles = [14, 24, [21, 48], [7, 34]]

After

derived = [[[21, 7, 1, 1], [21, 34, 28, 1], [48, 7, 41, 6], [48, 34, 14, 6]], [1, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S407

S409 · implies

Before

source roles = [14, 25, [21, 48], [8, 35]]

After

derived = [[[21, 8, 2, 12], [21, 35, 29, 12], [48, 8, 40, 5], [48, 35, 13, 5]], [5, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S408

S410 · implies

Before

source roles = [14, 26, [21, 48], [9, 36]]

After

derived = [[[21, 9, 3, 20], [21, 36, 30, 20], [48, 9, 39, 4], [48, 36, 12, 4]], [4, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S409

S411 · implies

Before

source roles = [15, 0, [22, 49], [0, 27]]

After

derived = [[[22, 0, 22, 15], [22, 27, 49, 15], [49, 0, 49, 15], [49, 27, 22, 15]], [15], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S410

S412 · implies

Before

source roles = [15, 1, [22, 49], [1, 28]]

After

derived = [[[22, 1, 23, 16], [22, 28, 50, 16], [49, 1, 48, 14], [49, 28, 21, 14]], [14, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S411

S413 · implies

Before

source roles = [15, 2, [22, 49], [10, 37]]

After

derived = [[[22, 10, 5, 22], [22, 37, 32, 22], [49, 10, 39, 4], [49, 37, 12, 4]], [4, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S412

S414 · implies

Before

source roles = [15, 3, [22, 49], [11, 38]]

After

derived = [[[22, 11, 6, 23], [22, 38, 33, 23], [49, 11, 38, 3], [49, 38, 11, 3]], [3, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S413

S415 · implies

Before

source roles = [15, 4, [22, 49], [12, 39]]

After

derived = [[[22, 12, 7, 24], [22, 39, 34, 24], [49, 12, 37, 2], [49, 39, 10, 2]], [2, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S414

S416 · implies

Before

source roles = [15, 5, [22, 49], [13, 40]]

After

derived = [[[22, 13, 8, 25], [22, 40, 35, 25], [49, 13, 36, 26], [49, 40, 9, 26]], [25, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S415

S417 · implies

Before

source roles = [15, 6, [22, 49], [14, 41]]

After

derived = [[[22, 14, 9, 26], [22, 41, 36, 26], [49, 14, 35, 25], [49, 41, 8, 25]], [25, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S416

S418 · implies

Before

source roles = [15, 7, [22, 49], [15, 42]]

After

derived = [[[22, 15, 10, 2], [22, 42, 37, 2], [49, 15, 34, 24], [49, 42, 7, 24]], [2, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S417

S419 · implies

Before

source roles = [15, 8, [22, 49], [16, 43]]

After

derived = [[[22, 16, 11, 3], [22, 43, 38, 3], [49, 16, 33, 23], [49, 43, 6, 23]], [3, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S418

S420 · implies

Before

source roles = [15, 9, [22, 49], [17, 44]]

After

derived = [[[22, 17, 12, 4], [22, 44, 39, 4], [49, 17, 32, 22], [49, 44, 5, 22]], [4, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S419

S421 · implies

Before

source roles = [15, 10, [22, 49], [18, 45]]

After

derived = [[[22, 18, 13, 5], [22, 45, 40, 5], [49, 18, 31, 21], [49, 45, 4, 21]], [5, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S420

S422 · implies

Before

source roles = [15, 11, [22, 49], [19, 46]]

After

derived = [[[22, 19, 14, 6], [22, 46, 41, 6], [49, 19, 30, 20], [49, 46, 3, 20]], [6, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S421

S423 · implies

Before

source roles = [15, 12, [22, 49], [2, 29]]

After

derived = [[[22, 2, 24, 17], [22, 29, 51, 17], [49, 2, 47, 13], [49, 29, 20, 13]], [13, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S422

S424 · implies

Before

source roles = [15, 13, [22, 49], [20, 47]]

After

derived = [[[22, 20, 15, 7], [22, 47, 42, 7], [49, 20, 29, 12], [49, 47, 2, 12]], [7, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S423

S425 · implies

Before

source roles = [15, 14, [22, 49], [21, 48]]

After

derived = [[[22, 21, 16, 8], [22, 48, 43, 8], [49, 21, 28, 1], [49, 48, 1, 1]], [1, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S424

S426 · implies

Before

source roles = [15, 15, [22, 49], [22, 49]]

After

derived = [[[22, 22, 17, 9], [22, 49, 44, 9], [49, 22, 27, 0], [49, 49, 0, 0]], [0, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S425

S427 · implies

Before

source roles = [15, 16, [22, 49], [23, 50]]

After

derived = [[[22, 23, 18, 10], [22, 50, 45, 10], [49, 23, 53, 19], [49, 50, 26, 19]], [10, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S426

S428 · implies

Before

source roles = [15, 17, [22, 49], [24, 51]]

After

derived = [[[22, 24, 19, 11], [22, 51, 46, 11], [49, 24, 52, 18], [49, 51, 25, 18]], [11, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S427

S429 · implies

Before

source roles = [15, 18, [22, 49], [25, 52]]

After

derived = [[[22, 25, 20, 13], [22, 52, 47, 13], [49, 25, 51, 17], [49, 52, 24, 17]], [13, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S428

S430 · implies

Before

source roles = [15, 19, [22, 49], [26, 53]]

After

derived = [[[22, 26, 21, 14], [22, 53, 48, 14], [49, 26, 50, 16], [49, 53, 23, 16]], [14, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S429

S431 · implies

Before

source roles = [15, 20, [22, 49], [3, 30]]

After

derived = [[[22, 3, 25, 18], [22, 30, 52, 18], [49, 3, 46, 11], [49, 30, 19, 11]], [11, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S430

S432 · implies

Before

source roles = [15, 21, [22, 49], [4, 31]]

After

derived = [[[22, 4, 26, 19], [22, 31, 53, 19], [49, 4, 45, 10], [49, 31, 18, 10]], [10, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S431

S433 · implies

Before

source roles = [15, 22, [22, 49], [5, 32]]

After

derived = [[[22, 5, 0, 0], [22, 32, 27, 0], [49, 5, 44, 9], [49, 32, 17, 9]], [0, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S432

S434 · implies

Before

source roles = [15, 23, [22, 49], [6, 33]]

After

derived = [[[22, 6, 1, 1], [22, 33, 28, 1], [49, 6, 43, 8], [49, 33, 16, 8]], [1, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S433

S435 · implies

Before

source roles = [15, 24, [22, 49], [7, 34]]

After

derived = [[[22, 7, 2, 12], [22, 34, 29, 12], [49, 7, 42, 7], [49, 34, 15, 7]], [7, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S434

S436 · implies

Before

source roles = [15, 25, [22, 49], [8, 35]]

After

derived = [[[22, 8, 3, 20], [22, 35, 30, 20], [49, 8, 41, 6], [49, 35, 14, 6]], [6, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S435

S437 · implies

Before

source roles = [15, 26, [22, 49], [9, 36]]

After

derived = [[[22, 9, 4, 21], [22, 36, 31, 21], [49, 9, 40, 5], [49, 36, 13, 5]], [5, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S436

S438 · implies

Before

source roles = [16, 0, [23, 50], [0, 27]]

After

derived = [[[23, 0, 23, 16], [23, 27, 50, 16], [50, 0, 50, 16], [50, 27, 23, 16]], [16], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S437

S439 · implies

Before

source roles = [16, 1, [23, 50], [1, 28]]

After

derived = [[[23, 1, 24, 17], [23, 28, 51, 17], [50, 1, 49, 15], [50, 28, 22, 15]], [15, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S438

S440 · implies

Before

source roles = [16, 2, [23, 50], [10, 37]]

After

derived = [[[23, 10, 6, 23], [23, 37, 33, 23], [50, 10, 40, 5], [50, 37, 13, 5]], [5, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S439

S441 · implies

Before

source roles = [16, 3, [23, 50], [11, 38]]

After

derived = [[[23, 11, 7, 24], [23, 38, 34, 24], [50, 11, 39, 4], [50, 38, 12, 4]], [4, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S440

S442 · implies

Before

source roles = [16, 4, [23, 50], [12, 39]]

After

derived = [[[23, 12, 8, 25], [23, 39, 35, 25], [50, 12, 38, 3], [50, 39, 11, 3]], [3, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S441

S443 · implies

Before

source roles = [16, 5, [23, 50], [13, 40]]

After

derived = [[[23, 13, 9, 26], [23, 40, 36, 26], [50, 13, 37, 2], [50, 40, 10, 2]], [2, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S442

S444 · implies

Before

source roles = [16, 6, [23, 50], [14, 41]]

After

derived = [[[23, 14, 10, 2], [23, 41, 37, 2], [50, 14, 36, 26], [50, 41, 9, 26]], [2, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S443

S445 · implies

Before

source roles = [16, 7, [23, 50], [15, 42]]

After

derived = [[[23, 15, 11, 3], [23, 42, 38, 3], [50, 15, 35, 25], [50, 42, 8, 25]], [3, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S444

S446 · implies

Before

source roles = [16, 8, [23, 50], [16, 43]]

After

derived = [[[23, 16, 12, 4], [23, 43, 39, 4], [50, 16, 34, 24], [50, 43, 7, 24]], [4, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S445

S447 · implies

Before

source roles = [16, 9, [23, 50], [17, 44]]

After

derived = [[[23, 17, 13, 5], [23, 44, 40, 5], [50, 17, 33, 23], [50, 44, 6, 23]], [5, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S446

S448 · implies

Before

source roles = [16, 10, [23, 50], [18, 45]]

After

derived = [[[23, 18, 14, 6], [23, 45, 41, 6], [50, 18, 32, 22], [50, 45, 5, 22]], [6, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S447

S449 · implies

Before

source roles = [16, 11, [23, 50], [19, 46]]

After

derived = [[[23, 19, 15, 7], [23, 46, 42, 7], [50, 19, 31, 21], [50, 46, 4, 21]], [7, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S448

S450 · implies

Before

source roles = [16, 12, [23, 50], [2, 29]]

After

derived = [[[23, 2, 25, 18], [23, 29, 52, 18], [50, 2, 48, 14], [50, 29, 21, 14]], [14, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S449

S451 · implies

Before

source roles = [16, 13, [23, 50], [20, 47]]

After

derived = [[[23, 20, 16, 8], [23, 47, 43, 8], [50, 20, 30, 20], [50, 47, 3, 20]], [8, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S450

S452 · implies

Before

source roles = [16, 14, [23, 50], [21, 48]]

After

derived = [[[23, 21, 17, 9], [23, 48, 44, 9], [50, 21, 29, 12], [50, 48, 2, 12]], [9, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S451

S453 · implies

Before

source roles = [16, 15, [23, 50], [22, 49]]

After

derived = [[[23, 22, 18, 10], [23, 49, 45, 10], [50, 22, 28, 1], [50, 49, 1, 1]], [1, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S452

S454 · implies

Before

source roles = [16, 16, [23, 50], [23, 50]]

After

derived = [[[23, 23, 19, 11], [23, 50, 46, 11], [50, 23, 27, 0], [50, 50, 0, 0]], [0, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S453

S455 · implies

Before

source roles = [16, 17, [23, 50], [24, 51]]

After

derived = [[[23, 24, 20, 13], [23, 51, 47, 13], [50, 24, 53, 19], [50, 51, 26, 19]], [13, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S454

S456 · implies

Before

source roles = [16, 18, [23, 50], [25, 52]]

After

derived = [[[23, 25, 21, 14], [23, 52, 48, 14], [50, 25, 52, 18], [50, 52, 25, 18]], [14, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S455

S457 · implies

Before

source roles = [16, 19, [23, 50], [26, 53]]

After

derived = [[[23, 26, 22, 15], [23, 53, 49, 15], [50, 26, 51, 17], [50, 53, 24, 17]], [15, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S456

S458 · implies

Before

source roles = [16, 20, [23, 50], [3, 30]]

After

derived = [[[23, 3, 26, 19], [23, 30, 53, 19], [50, 3, 47, 13], [50, 30, 20, 13]], [13, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S457

S459 · implies

Before

source roles = [16, 21, [23, 50], [4, 31]]

After

derived = [[[23, 4, 0, 0], [23, 31, 27, 0], [50, 4, 46, 11], [50, 31, 19, 11]], [0, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S458

S460 · implies

Before

source roles = [16, 22, [23, 50], [5, 32]]

After

derived = [[[23, 5, 1, 1], [23, 32, 28, 1], [50, 5, 45, 10], [50, 32, 18, 10]], [1, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S459

S461 · implies

Before

source roles = [16, 23, [23, 50], [6, 33]]

After

derived = [[[23, 6, 2, 12], [23, 33, 29, 12], [50, 6, 44, 9], [50, 33, 17, 9]], [9, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S460

S462 · implies

Before

source roles = [16, 24, [23, 50], [7, 34]]

After

derived = [[[23, 7, 3, 20], [23, 34, 30, 20], [50, 7, 43, 8], [50, 34, 16, 8]], [8, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S461

S463 · implies

Before

source roles = [16, 25, [23, 50], [8, 35]]

After

derived = [[[23, 8, 4, 21], [23, 35, 31, 21], [50, 8, 42, 7], [50, 35, 15, 7]], [7, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S462

S464 · implies

Before

source roles = [16, 26, [23, 50], [9, 36]]

After

derived = [[[23, 9, 5, 22], [23, 36, 32, 22], [50, 9, 41, 6], [50, 36, 14, 6]], [6, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S463

S465 · implies

Before

source roles = [17, 0, [24, 51], [0, 27]]

After

derived = [[[24, 0, 24, 17], [24, 27, 51, 17], [51, 0, 51, 17], [51, 27, 24, 17]], [17], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S464

S466 · implies

Before

source roles = [17, 1, [24, 51], [1, 28]]

After

derived = [[[24, 1, 25, 18], [24, 28, 52, 18], [51, 1, 50, 16], [51, 28, 23, 16]], [16, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S465

S467 · implies

Before

source roles = [17, 2, [24, 51], [10, 37]]

After

derived = [[[24, 10, 7, 24], [24, 37, 34, 24], [51, 10, 41, 6], [51, 37, 14, 6]], [6, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S466

S468 · implies

Before

source roles = [17, 3, [24, 51], [11, 38]]

After

derived = [[[24, 11, 8, 25], [24, 38, 35, 25], [51, 11, 40, 5], [51, 38, 13, 5]], [5, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S467

S469 · implies

Before

source roles = [17, 4, [24, 51], [12, 39]]

After

derived = [[[24, 12, 9, 26], [24, 39, 36, 26], [51, 12, 39, 4], [51, 39, 12, 4]], [4, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S468

S470 · implies

Before

source roles = [17, 5, [24, 51], [13, 40]]

After

derived = [[[24, 13, 10, 2], [24, 40, 37, 2], [51, 13, 38, 3], [51, 40, 11, 3]], [2, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S469

S471 · implies

Before

source roles = [17, 6, [24, 51], [14, 41]]

After

derived = [[[24, 14, 11, 3], [24, 41, 38, 3], [51, 14, 37, 2], [51, 41, 10, 2]], [2, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S470

S472 · implies

Before

source roles = [17, 7, [24, 51], [15, 42]]

After

derived = [[[24, 15, 12, 4], [24, 42, 39, 4], [51, 15, 36, 26], [51, 42, 9, 26]], [4, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S471

S473 · implies

Before

source roles = [17, 8, [24, 51], [16, 43]]

After

derived = [[[24, 16, 13, 5], [24, 43, 40, 5], [51, 16, 35, 25], [51, 43, 8, 25]], [5, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S472

S474 · implies

Before

source roles = [17, 9, [24, 51], [17, 44]]

After

derived = [[[24, 17, 14, 6], [24, 44, 41, 6], [51, 17, 34, 24], [51, 44, 7, 24]], [6, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S473

S475 · implies

Before

source roles = [17, 10, [24, 51], [18, 45]]

After

derived = [[[24, 18, 15, 7], [24, 45, 42, 7], [51, 18, 33, 23], [51, 45, 6, 23]], [7, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S474

S476 · implies

Before

source roles = [17, 11, [24, 51], [19, 46]]

After

derived = [[[24, 19, 16, 8], [24, 46, 43, 8], [51, 19, 32, 22], [51, 46, 5, 22]], [8, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S475

S477 · implies

Before

source roles = [17, 12, [24, 51], [2, 29]]

After

derived = [[[24, 2, 26, 19], [24, 29, 53, 19], [51, 2, 49, 15], [51, 29, 22, 15]], [15, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S476

S478 · implies

Before

source roles = [17, 13, [24, 51], [20, 47]]

After

derived = [[[24, 20, 17, 9], [24, 47, 44, 9], [51, 20, 31, 21], [51, 47, 4, 21]], [9, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S477

S479 · implies

Before

source roles = [17, 14, [24, 51], [21, 48]]

After

derived = [[[24, 21, 18, 10], [24, 48, 45, 10], [51, 21, 30, 20], [51, 48, 3, 20]], [10, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S478

S480 · implies

Before

source roles = [17, 15, [24, 51], [22, 49]]

After

derived = [[[24, 22, 19, 11], [24, 49, 46, 11], [51, 22, 29, 12], [51, 49, 2, 12]], [11, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S479

S481 · implies

Before

source roles = [17, 16, [24, 51], [23, 50]]

After

derived = [[[24, 23, 20, 13], [24, 50, 47, 13], [51, 23, 28, 1], [51, 50, 1, 1]], [1, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S480

S482 · implies

Before

source roles = [17, 17, [24, 51], [24, 51]]

After

derived = [[[24, 24, 21, 14], [24, 51, 48, 14], [51, 24, 27, 0], [51, 51, 0, 0]], [0, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S481

S483 · implies

Before

source roles = [17, 18, [24, 51], [25, 52]]

After

derived = [[[24, 25, 22, 15], [24, 52, 49, 15], [51, 25, 53, 19], [51, 52, 26, 19]], [15, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S482

S484 · implies

Before

source roles = [17, 19, [24, 51], [26, 53]]

After

derived = [[[24, 26, 23, 16], [24, 53, 50, 16], [51, 26, 52, 18], [51, 53, 25, 18]], [16, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S483

S485 · implies

Before

source roles = [17, 20, [24, 51], [3, 30]]

After

derived = [[[24, 3, 0, 0], [24, 30, 27, 0], [51, 3, 48, 14], [51, 30, 21, 14]], [0, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S484

S486 · implies

Before

source roles = [17, 21, [24, 51], [4, 31]]

After

derived = [[[24, 4, 1, 1], [24, 31, 28, 1], [51, 4, 47, 13], [51, 31, 20, 13]], [1, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S485

S487 · implies

Before

source roles = [17, 22, [24, 51], [5, 32]]

After

derived = [[[24, 5, 2, 12], [24, 32, 29, 12], [51, 5, 46, 11], [51, 32, 19, 11]], [11, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S486

S488 · implies

Before

source roles = [17, 23, [24, 51], [6, 33]]

After

derived = [[[24, 6, 3, 20], [24, 33, 30, 20], [51, 6, 45, 10], [51, 33, 18, 10]], [10, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S487

S489 · implies

Before

source roles = [17, 24, [24, 51], [7, 34]]

After

derived = [[[24, 7, 4, 21], [24, 34, 31, 21], [51, 7, 44, 9], [51, 34, 17, 9]], [9, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S488

S490 · implies

Before

source roles = [17, 25, [24, 51], [8, 35]]

After

derived = [[[24, 8, 5, 22], [24, 35, 32, 22], [51, 8, 43, 8], [51, 35, 16, 8]], [8, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S489

S491 · implies

Before

source roles = [17, 26, [24, 51], [9, 36]]

After

derived = [[[24, 9, 6, 23], [24, 36, 33, 23], [51, 9, 42, 7], [51, 36, 15, 7]], [7, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S490

S492 · implies

Before

source roles = [18, 0, [25, 52], [0, 27]]

After

derived = [[[25, 0, 25, 18], [25, 27, 52, 18], [52, 0, 52, 18], [52, 27, 25, 18]], [18], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S491

S493 · implies

Before

source roles = [18, 1, [25, 52], [1, 28]]

After

derived = [[[25, 1, 26, 19], [25, 28, 53, 19], [52, 1, 51, 17], [52, 28, 24, 17]], [17, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S492

S494 · implies

Before

source roles = [18, 2, [25, 52], [10, 37]]

After

derived = [[[25, 10, 8, 25], [25, 37, 35, 25], [52, 10, 42, 7], [52, 37, 15, 7]], [7, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S493

S495 · implies

Before

source roles = [18, 3, [25, 52], [11, 38]]

After

derived = [[[25, 11, 9, 26], [25, 38, 36, 26], [52, 11, 41, 6], [52, 38, 14, 6]], [6, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S494

S496 · implies

Before

source roles = [18, 4, [25, 52], [12, 39]]

After

derived = [[[25, 12, 10, 2], [25, 39, 37, 2], [52, 12, 40, 5], [52, 39, 13, 5]], [2, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S495

S497 · implies

Before

source roles = [18, 5, [25, 52], [13, 40]]

After

derived = [[[25, 13, 11, 3], [25, 40, 38, 3], [52, 13, 39, 4], [52, 40, 12, 4]], [3, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S496

S498 · implies

Before

source roles = [18, 6, [25, 52], [14, 41]]

After

derived = [[[25, 14, 12, 4], [25, 41, 39, 4], [52, 14, 38, 3], [52, 41, 11, 3]], [3, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S497

S499 · implies

Before

source roles = [18, 7, [25, 52], [15, 42]]

After

derived = [[[25, 15, 13, 5], [25, 42, 40, 5], [52, 15, 37, 2], [52, 42, 10, 2]], [2, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S498

S500 · implies

Before

source roles = [18, 8, [25, 52], [16, 43]]

After

derived = [[[25, 16, 14, 6], [25, 43, 41, 6], [52, 16, 36, 26], [52, 43, 9, 26]], [6, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S499

S501 · implies

Before

source roles = [18, 9, [25, 52], [17, 44]]

After

derived = [[[25, 17, 15, 7], [25, 44, 42, 7], [52, 17, 35, 25], [52, 44, 8, 25]], [7, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S500

S502 · implies

Before

source roles = [18, 10, [25, 52], [18, 45]]

After

derived = [[[25, 18, 16, 8], [25, 45, 43, 8], [52, 18, 34, 24], [52, 45, 7, 24]], [8, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S501

S503 · implies

Before

source roles = [18, 11, [25, 52], [19, 46]]

After

derived = [[[25, 19, 17, 9], [25, 46, 44, 9], [52, 19, 33, 23], [52, 46, 6, 23]], [9, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S502

S504 · implies

Before

source roles = [18, 12, [25, 52], [2, 29]]

After

derived = [[[25, 2, 0, 0], [25, 29, 27, 0], [52, 2, 50, 16], [52, 29, 23, 16]], [0, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S503

S505 · implies

Before

source roles = [18, 13, [25, 52], [20, 47]]

After

derived = [[[25, 20, 18, 10], [25, 47, 45, 10], [52, 20, 32, 22], [52, 47, 5, 22]], [10, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S504

S506 · implies

Before

source roles = [18, 14, [25, 52], [21, 48]]

After

derived = [[[25, 21, 19, 11], [25, 48, 46, 11], [52, 21, 31, 21], [52, 48, 4, 21]], [11, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S505

S507 · implies

Before

source roles = [18, 15, [25, 52], [22, 49]]

After

derived = [[[25, 22, 20, 13], [25, 49, 47, 13], [52, 22, 30, 20], [52, 49, 3, 20]], [13, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S506

S508 · implies

Before

source roles = [18, 16, [25, 52], [23, 50]]

After

derived = [[[25, 23, 21, 14], [25, 50, 48, 14], [52, 23, 29, 12], [52, 50, 2, 12]], [12, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S507

S509 · implies

Before

source roles = [18, 17, [25, 52], [24, 51]]

After

derived = [[[25, 24, 22, 15], [25, 51, 49, 15], [52, 24, 28, 1], [52, 51, 1, 1]], [1, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S508

S510 · implies

Before

source roles = [18, 18, [25, 52], [25, 52]]

After

derived = [[[25, 25, 23, 16], [25, 52, 50, 16], [52, 25, 27, 0], [52, 52, 0, 0]], [0, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S509

S511 · implies

Before

source roles = [18, 19, [25, 52], [26, 53]]

After

derived = [[[25, 26, 24, 17], [25, 53, 51, 17], [52, 26, 53, 19], [52, 53, 26, 19]], [17, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S510

S512 · implies

Before

source roles = [18, 20, [25, 52], [3, 30]]

After

derived = [[[25, 3, 1, 1], [25, 30, 28, 1], [52, 3, 49, 15], [52, 30, 22, 15]], [1, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S511

S513 · implies

Before

source roles = [18, 21, [25, 52], [4, 31]]

After

derived = [[[25, 4, 2, 12], [25, 31, 29, 12], [52, 4, 48, 14], [52, 31, 21, 14]], [12, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S512

S514 · implies

Before

source roles = [18, 22, [25, 52], [5, 32]]

After

derived = [[[25, 5, 3, 20], [25, 32, 30, 20], [52, 5, 47, 13], [52, 32, 20, 13]], [13, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S513

S515 · implies

Before

source roles = [18, 23, [25, 52], [6, 33]]

After

derived = [[[25, 6, 4, 21], [25, 33, 31, 21], [52, 6, 46, 11], [52, 33, 19, 11]], [11, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S514

S516 · implies

Before

source roles = [18, 24, [25, 52], [7, 34]]

After

derived = [[[25, 7, 5, 22], [25, 34, 32, 22], [52, 7, 45, 10], [52, 34, 18, 10]], [10, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S515

S517 · implies

Before

source roles = [18, 25, [25, 52], [8, 35]]

After

derived = [[[25, 8, 6, 23], [25, 35, 33, 23], [52, 8, 44, 9], [52, 35, 17, 9]], [9, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S516

S518 · implies

Before

source roles = [18, 26, [25, 52], [9, 36]]

After

derived = [[[25, 9, 7, 24], [25, 36, 34, 24], [52, 9, 43, 8], [52, 36, 16, 8]], [8, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S517

S519 · implies

Before

source roles = [19, 0, [26, 53], [0, 27]]

After

derived = [[[26, 0, 26, 19], [26, 27, 53, 19], [53, 0, 53, 19], [53, 27, 26, 19]], [19], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S518

S520 · implies

Before

source roles = [19, 1, [26, 53], [1, 28]]

After

derived = [[[26, 1, 0, 0], [26, 28, 27, 0], [53, 1, 52, 18], [53, 28, 25, 18]], [0, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S519

S521 · implies

Before

source roles = [19, 2, [26, 53], [10, 37]]

After

derived = [[[26, 10, 9, 26], [26, 37, 36, 26], [53, 10, 43, 8], [53, 37, 16, 8]], [8, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S520

S522 · implies

Before

source roles = [19, 3, [26, 53], [11, 38]]

After

derived = [[[26, 11, 10, 2], [26, 38, 37, 2], [53, 11, 42, 7], [53, 38, 15, 7]], [2, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S521

S523 · implies

Before

source roles = [19, 4, [26, 53], [12, 39]]

After

derived = [[[26, 12, 11, 3], [26, 39, 38, 3], [53, 12, 41, 6], [53, 39, 14, 6]], [3, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S522

S524 · implies

Before

source roles = [19, 5, [26, 53], [13, 40]]

After

derived = [[[26, 13, 12, 4], [26, 40, 39, 4], [53, 13, 40, 5], [53, 40, 13, 5]], [4, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S523

S525 · implies

Before

source roles = [19, 6, [26, 53], [14, 41]]

After

derived = [[[26, 14, 13, 5], [26, 41, 40, 5], [53, 14, 39, 4], [53, 41, 12, 4]], [4, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S524

S526 · implies

Before

source roles = [19, 7, [26, 53], [15, 42]]

After

derived = [[[26, 15, 14, 6], [26, 42, 41, 6], [53, 15, 38, 3], [53, 42, 11, 3]], [3, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S525

S527 · implies

Before

source roles = [19, 8, [26, 53], [16, 43]]

After

derived = [[[26, 16, 15, 7], [26, 43, 42, 7], [53, 16, 37, 2], [53, 43, 10, 2]], [2, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S526

S528 · implies

Before

source roles = [19, 9, [26, 53], [17, 44]]

After

derived = [[[26, 17, 16, 8], [26, 44, 43, 8], [53, 17, 36, 26], [53, 44, 9, 26]], [8, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S527

S529 · implies

Before

source roles = [19, 10, [26, 53], [18, 45]]

After

derived = [[[26, 18, 17, 9], [26, 45, 44, 9], [53, 18, 35, 25], [53, 45, 8, 25]], [9, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S528

S530 · implies

Before

source roles = [19, 11, [26, 53], [19, 46]]

After

derived = [[[26, 19, 18, 10], [26, 46, 45, 10], [53, 19, 34, 24], [53, 46, 7, 24]], [10, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S529

S531 · implies

Before

source roles = [19, 12, [26, 53], [2, 29]]

After

derived = [[[26, 2, 1, 1], [26, 29, 28, 1], [53, 2, 51, 17], [53, 29, 24, 17]], [1, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S530

S532 · implies

Before

source roles = [19, 13, [26, 53], [20, 47]]

After

derived = [[[26, 20, 19, 11], [26, 47, 46, 11], [53, 20, 33, 23], [53, 47, 6, 23]], [11, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S531

S533 · implies

Before

source roles = [19, 14, [26, 53], [21, 48]]

After

derived = [[[26, 21, 20, 13], [26, 48, 47, 13], [53, 21, 32, 22], [53, 48, 5, 22]], [13, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S532

S534 · implies

Before

source roles = [19, 15, [26, 53], [22, 49]]

After

derived = [[[26, 22, 21, 14], [26, 49, 48, 14], [53, 22, 31, 21], [53, 49, 4, 21]], [14, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S533

S535 · implies

Before

source roles = [19, 16, [26, 53], [23, 50]]

After

derived = [[[26, 23, 22, 15], [26, 50, 49, 15], [53, 23, 30, 20], [53, 50, 3, 20]], [15, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S534

S536 · implies

Before

source roles = [19, 17, [26, 53], [24, 51]]

After

derived = [[[26, 24, 23, 16], [26, 51, 50, 16], [53, 24, 29, 12], [53, 51, 2, 12]], [12, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S535

S537 · implies

Before

source roles = [19, 18, [26, 53], [25, 52]]

After

derived = [[[26, 25, 24, 17], [26, 52, 51, 17], [53, 25, 28, 1], [53, 52, 1, 1]], [1, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S536

S538 · implies

Before

source roles = [19, 19, [26, 53], [26, 53]]

After

derived = [[[26, 26, 25, 18], [26, 53, 52, 18], [53, 26, 27, 0], [53, 53, 0, 0]], [0, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S537

S539 · implies

Before

source roles = [19, 20, [26, 53], [3, 30]]

After

derived = [[[26, 3, 2, 12], [26, 30, 29, 12], [53, 3, 50, 16], [53, 30, 23, 16]], [12, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S538

S540 · implies

Before

source roles = [19, 21, [26, 53], [4, 31]]

After

derived = [[[26, 4, 3, 20], [26, 31, 30, 20], [53, 4, 49, 15], [53, 31, 22, 15]], [15, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S539

S541 · implies

Before

source roles = [19, 22, [26, 53], [5, 32]]

After

derived = [[[26, 5, 4, 21], [26, 32, 31, 21], [53, 5, 48, 14], [53, 32, 21, 14]], [14, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S540

S542 · implies

Before

source roles = [19, 23, [26, 53], [6, 33]]

After

derived = [[[26, 6, 5, 22], [26, 33, 32, 22], [53, 6, 47, 13], [53, 33, 20, 13]], [13, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S541

S543 · implies

Before

source roles = [19, 24, [26, 53], [7, 34]]

After

derived = [[[26, 7, 6, 23], [26, 34, 33, 23], [53, 7, 46, 11], [53, 34, 19, 11]], [11, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S542

S544 · implies

Before

source roles = [19, 25, [26, 53], [8, 35]]

After

derived = [[[26, 8, 7, 24], [26, 35, 34, 24], [53, 8, 45, 10], [53, 35, 18, 10]], [10, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S543

S545 · implies

Before

source roles = [19, 26, [26, 53], [9, 36]]

After

derived = [[[26, 9, 8, 25], [26, 36, 35, 25], [53, 9, 44, 9], [53, 36, 17, 9]], [9, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S544

S546 · implies

Before

source roles = [20, 0, [3, 30], [0, 27]]

After

derived = [[[3, 0, 3, 20], [3, 27, 30, 20], [30, 0, 30, 20], [30, 27, 3, 20]], [20], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S545

S547 · implies

Before

source roles = [20, 1, [3, 30], [1, 28]]

After

derived = [[[3, 1, 4, 21], [3, 28, 31, 21], [30, 1, 29, 12], [30, 28, 2, 12]], [12, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S546

S548 · implies

Before

source roles = [20, 2, [3, 30], [10, 37]]

After

derived = [[[3, 10, 13, 5], [3, 37, 40, 5], [30, 10, 47, 13], [30, 37, 20, 13]], [5, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S547

S549 · implies

Before

source roles = [20, 3, [3, 30], [11, 38]]

After

derived = [[[3, 11, 14, 6], [3, 38, 41, 6], [30, 11, 46, 11], [30, 38, 19, 11]], [6, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S548

S550 · implies

Before

source roles = [20, 4, [3, 30], [12, 39]]

After

derived = [[[3, 12, 15, 7], [3, 39, 42, 7], [30, 12, 45, 10], [30, 39, 18, 10]], [7, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S549

S551 · implies

Before

source roles = [20, 5, [3, 30], [13, 40]]

After

derived = [[[3, 13, 16, 8], [3, 40, 43, 8], [30, 13, 44, 9], [30, 40, 17, 9]], [8, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S550

S552 · implies

Before

source roles = [20, 6, [3, 30], [14, 41]]

After

derived = [[[3, 14, 17, 9], [3, 41, 44, 9], [30, 14, 43, 8], [30, 41, 16, 8]], [8, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S551

S553 · implies

Before

source roles = [20, 7, [3, 30], [15, 42]]

After

derived = [[[3, 15, 18, 10], [3, 42, 45, 10], [30, 15, 42, 7], [30, 42, 15, 7]], [7, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S552

S554 · implies

Before

source roles = [20, 8, [3, 30], [16, 43]]

After

derived = [[[3, 16, 19, 11], [3, 43, 46, 11], [30, 16, 41, 6], [30, 43, 14, 6]], [6, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S553

S555 · implies

Before

source roles = [20, 9, [3, 30], [17, 44]]

After

derived = [[[3, 17, 20, 13], [3, 44, 47, 13], [30, 17, 40, 5], [30, 44, 13, 5]], [5, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S554

S556 · implies

Before

source roles = [20, 10, [3, 30], [18, 45]]

After

derived = [[[3, 18, 21, 14], [3, 45, 48, 14], [30, 18, 39, 4], [30, 45, 12, 4]], [4, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S555

S557 · implies

Before

source roles = [20, 11, [3, 30], [19, 46]]

After

derived = [[[3, 19, 22, 15], [3, 46, 49, 15], [30, 19, 38, 3], [30, 46, 11, 3]], [3, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S556

S558 · implies

Before

source roles = [20, 12, [3, 30], [2, 29]]

After

derived = [[[3, 2, 5, 22], [3, 29, 32, 22], [30, 2, 28, 1], [30, 29, 1, 1]], [1, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S557

S559 · implies

Before

source roles = [20, 13, [3, 30], [20, 47]]

After

derived = [[[3, 20, 23, 16], [3, 47, 50, 16], [30, 20, 37, 2], [30, 47, 10, 2]], [2, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S558

S560 · implies

Before

source roles = [20, 14, [3, 30], [21, 48]]

After

derived = [[[3, 21, 24, 17], [3, 48, 51, 17], [30, 21, 36, 26], [30, 48, 9, 26]], [17, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S559

S561 · implies

Before

source roles = [20, 15, [3, 30], [22, 49]]

After

derived = [[[3, 22, 25, 18], [3, 49, 52, 18], [30, 22, 35, 25], [30, 49, 8, 25]], [18, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S560

S562 · implies

Before

source roles = [20, 16, [3, 30], [23, 50]]

After

derived = [[[3, 23, 26, 19], [3, 50, 53, 19], [30, 23, 34, 24], [30, 50, 7, 24]], [19, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S561

S563 · implies

Before

source roles = [20, 17, [3, 30], [24, 51]]

After

derived = [[[3, 24, 0, 0], [3, 51, 27, 0], [30, 24, 33, 23], [30, 51, 6, 23]], [0, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S562

S564 · implies

Before

source roles = [20, 18, [3, 30], [25, 52]]

After

derived = [[[3, 25, 1, 1], [3, 52, 28, 1], [30, 25, 32, 22], [30, 52, 5, 22]], [1, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S563

S565 · implies

Before

source roles = [20, 19, [3, 30], [26, 53]]

After

derived = [[[3, 26, 2, 12], [3, 53, 29, 12], [30, 26, 31, 21], [30, 53, 4, 21]], [12, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S564

S566 · implies

Before

source roles = [20, 20, [3, 30], [3, 30]]

After

derived = [[[3, 3, 6, 23], [3, 30, 33, 23], [30, 3, 27, 0], [30, 30, 0, 0]], [0, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S565

S567 · implies

Before

source roles = [20, 21, [3, 30], [4, 31]]

After

derived = [[[3, 4, 7, 24], [3, 31, 34, 24], [30, 4, 53, 19], [30, 31, 26, 19]], [19, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S566

S568 · implies

Before

source roles = [20, 22, [3, 30], [5, 32]]

After

derived = [[[3, 5, 8, 25], [3, 32, 35, 25], [30, 5, 52, 18], [30, 32, 25, 18]], [18, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S567

S569 · implies

Before

source roles = [20, 23, [3, 30], [6, 33]]

After

derived = [[[3, 6, 9, 26], [3, 33, 36, 26], [30, 6, 51, 17], [30, 33, 24, 17]], [17, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S568

S570 · implies

Before

source roles = [20, 24, [3, 30], [7, 34]]

After

derived = [[[3, 7, 10, 2], [3, 34, 37, 2], [30, 7, 50, 16], [30, 34, 23, 16]], [2, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S569

S571 · implies

Before

source roles = [20, 25, [3, 30], [8, 35]]

After

derived = [[[3, 8, 11, 3], [3, 35, 38, 3], [30, 8, 49, 15], [30, 35, 22, 15]], [3, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S570

S572 · implies

Before

source roles = [20, 26, [3, 30], [9, 36]]

After

derived = [[[3, 9, 12, 4], [3, 36, 39, 4], [30, 9, 48, 14], [30, 36, 21, 14]], [4, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S571

S573 · implies

Before

source roles = [21, 0, [4, 31], [0, 27]]

After

derived = [[[4, 0, 4, 21], [4, 27, 31, 21], [31, 0, 31, 21], [31, 27, 4, 21]], [21], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S572

S574 · implies

Before

source roles = [21, 1, [4, 31], [1, 28]]

After

derived = [[[4, 1, 5, 22], [4, 28, 32, 22], [31, 1, 30, 20], [31, 28, 3, 20]], [20, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S573

S575 · implies

Before

source roles = [21, 2, [4, 31], [10, 37]]

After

derived = [[[4, 10, 14, 6], [4, 37, 41, 6], [31, 10, 48, 14], [31, 37, 21, 14]], [6, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S574

S576 · implies

Before

source roles = [21, 3, [4, 31], [11, 38]]

After

derived = [[[4, 11, 15, 7], [4, 38, 42, 7], [31, 11, 47, 13], [31, 38, 20, 13]], [7, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S575

S577 · implies

Before

source roles = [21, 4, [4, 31], [12, 39]]

After

derived = [[[4, 12, 16, 8], [4, 39, 43, 8], [31, 12, 46, 11], [31, 39, 19, 11]], [8, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S576

S578 · implies

Before

source roles = [21, 5, [4, 31], [13, 40]]

After

derived = [[[4, 13, 17, 9], [4, 40, 44, 9], [31, 13, 45, 10], [31, 40, 18, 10]], [9, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S577

S579 · implies

Before

source roles = [21, 6, [4, 31], [14, 41]]

After

derived = [[[4, 14, 18, 10], [4, 41, 45, 10], [31, 14, 44, 9], [31, 41, 17, 9]], [9, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S578

S580 · implies

Before

source roles = [21, 7, [4, 31], [15, 42]]

After

derived = [[[4, 15, 19, 11], [4, 42, 46, 11], [31, 15, 43, 8], [31, 42, 16, 8]], [8, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S579

S581 · implies

Before

source roles = [21, 8, [4, 31], [16, 43]]

After

derived = [[[4, 16, 20, 13], [4, 43, 47, 13], [31, 16, 42, 7], [31, 43, 15, 7]], [7, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S580

S582 · implies

Before

source roles = [21, 9, [4, 31], [17, 44]]

After

derived = [[[4, 17, 21, 14], [4, 44, 48, 14], [31, 17, 41, 6], [31, 44, 14, 6]], [6, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S581

S583 · implies

Before

source roles = [21, 10, [4, 31], [18, 45]]

After

derived = [[[4, 18, 22, 15], [4, 45, 49, 15], [31, 18, 40, 5], [31, 45, 13, 5]], [5, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S582

S584 · implies

Before

source roles = [21, 11, [4, 31], [19, 46]]

After

derived = [[[4, 19, 23, 16], [4, 46, 50, 16], [31, 19, 39, 4], [31, 46, 12, 4]], [4, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S583

S585 · implies

Before

source roles = [21, 12, [4, 31], [2, 29]]

After

derived = [[[4, 2, 6, 23], [4, 29, 33, 23], [31, 2, 29, 12], [31, 29, 2, 12]], [12, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S584

S586 · implies

Before

source roles = [21, 13, [4, 31], [20, 47]]

After

derived = [[[4, 20, 24, 17], [4, 47, 51, 17], [31, 20, 38, 3], [31, 47, 11, 3]], [3, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S585

S587 · implies

Before

source roles = [21, 14, [4, 31], [21, 48]]

After

derived = [[[4, 21, 25, 18], [4, 48, 52, 18], [31, 21, 37, 2], [31, 48, 10, 2]], [2, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S586

S588 · implies

Before

source roles = [21, 15, [4, 31], [22, 49]]

After

derived = [[[4, 22, 26, 19], [4, 49, 53, 19], [31, 22, 36, 26], [31, 49, 9, 26]], [19, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S587

S589 · implies

Before

source roles = [21, 16, [4, 31], [23, 50]]

After

derived = [[[4, 23, 0, 0], [4, 50, 27, 0], [31, 23, 35, 25], [31, 50, 8, 25]], [0, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S588

S590 · implies

Before

source roles = [21, 17, [4, 31], [24, 51]]

After

derived = [[[4, 24, 1, 1], [4, 51, 28, 1], [31, 24, 34, 24], [31, 51, 7, 24]], [1, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S589

S591 · implies

Before

source roles = [21, 18, [4, 31], [25, 52]]

After

derived = [[[4, 25, 2, 12], [4, 52, 29, 12], [31, 25, 33, 23], [31, 52, 6, 23]], [12, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S590

S592 · implies

Before

source roles = [21, 19, [4, 31], [26, 53]]

After

derived = [[[4, 26, 3, 20], [4, 53, 30, 20], [31, 26, 32, 22], [31, 53, 5, 22]], [20, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S591

S593 · implies

Before

source roles = [21, 20, [4, 31], [3, 30]]

After

derived = [[[4, 3, 7, 24], [4, 30, 34, 24], [31, 3, 28, 1], [31, 30, 1, 1]], [1, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S592

S594 · implies

Before

source roles = [21, 21, [4, 31], [4, 31]]

After

derived = [[[4, 4, 8, 25], [4, 31, 35, 25], [31, 4, 27, 0], [31, 31, 0, 0]], [0, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S593

S595 · implies

Before

source roles = [21, 22, [4, 31], [5, 32]]

After

derived = [[[4, 5, 9, 26], [4, 32, 36, 26], [31, 5, 53, 19], [31, 32, 26, 19]], [19, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S594

S596 · implies

Before

source roles = [21, 23, [4, 31], [6, 33]]

After

derived = [[[4, 6, 10, 2], [4, 33, 37, 2], [31, 6, 52, 18], [31, 33, 25, 18]], [2, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S595

S597 · implies

Before

source roles = [21, 24, [4, 31], [7, 34]]

After

derived = [[[4, 7, 11, 3], [4, 34, 38, 3], [31, 7, 51, 17], [31, 34, 24, 17]], [3, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S596

S598 · implies

Before

source roles = [21, 25, [4, 31], [8, 35]]

After

derived = [[[4, 8, 12, 4], [4, 35, 39, 4], [31, 8, 50, 16], [31, 35, 23, 16]], [4, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S597

S599 · implies

Before

source roles = [21, 26, [4, 31], [9, 36]]

After

derived = [[[4, 9, 13, 5], [4, 36, 40, 5], [31, 9, 49, 15], [31, 36, 22, 15]], [5, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S598

S600 · implies

Before

source roles = [22, 0, [5, 32], [0, 27]]

After

derived = [[[5, 0, 5, 22], [5, 27, 32, 22], [32, 0, 32, 22], [32, 27, 5, 22]], [22], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S599

S601 · implies

Before

source roles = [22, 1, [5, 32], [1, 28]]

After

derived = [[[5, 1, 6, 23], [5, 28, 33, 23], [32, 1, 31, 21], [32, 28, 4, 21]], [21, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S600

S602 · implies

Before

source roles = [22, 2, [5, 32], [10, 37]]

After

derived = [[[5, 10, 15, 7], [5, 37, 42, 7], [32, 10, 49, 15], [32, 37, 22, 15]], [7, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S601

S603 · implies

Before

source roles = [22, 3, [5, 32], [11, 38]]

After

derived = [[[5, 11, 16, 8], [5, 38, 43, 8], [32, 11, 48, 14], [32, 38, 21, 14]], [8, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S602

S604 · implies

Before

source roles = [22, 4, [5, 32], [12, 39]]

After

derived = [[[5, 12, 17, 9], [5, 39, 44, 9], [32, 12, 47, 13], [32, 39, 20, 13]], [9, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S603

S605 · implies

Before

source roles = [22, 5, [5, 32], [13, 40]]

After

derived = [[[5, 13, 18, 10], [5, 40, 45, 10], [32, 13, 46, 11], [32, 40, 19, 11]], [10, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S604

S606 · implies

Before

source roles = [22, 6, [5, 32], [14, 41]]

After

derived = [[[5, 14, 19, 11], [5, 41, 46, 11], [32, 14, 45, 10], [32, 41, 18, 10]], [10, 11], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S605

S607 · implies

Before

source roles = [22, 7, [5, 32], [15, 42]]

After

derived = [[[5, 15, 20, 13], [5, 42, 47, 13], [32, 15, 44, 9], [32, 42, 17, 9]], [9, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S606

S608 · implies

Before

source roles = [22, 8, [5, 32], [16, 43]]

After

derived = [[[5, 16, 21, 14], [5, 43, 48, 14], [32, 16, 43, 8], [32, 43, 16, 8]], [8, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S607

S609 · implies

Before

source roles = [22, 9, [5, 32], [17, 44]]

After

derived = [[[5, 17, 22, 15], [5, 44, 49, 15], [32, 17, 42, 7], [32, 44, 15, 7]], [7, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S608

S610 · implies

Before

source roles = [22, 10, [5, 32], [18, 45]]

After

derived = [[[5, 18, 23, 16], [5, 45, 50, 16], [32, 18, 41, 6], [32, 45, 14, 6]], [6, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S609

S611 · implies

Before

source roles = [22, 11, [5, 32], [19, 46]]

After

derived = [[[5, 19, 24, 17], [5, 46, 51, 17], [32, 19, 40, 5], [32, 46, 13, 5]], [5, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S610

S612 · implies

Before

source roles = [22, 12, [5, 32], [2, 29]]

After

derived = [[[5, 2, 7, 24], [5, 29, 34, 24], [32, 2, 30, 20], [32, 29, 3, 20]], [20, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S611

S613 · implies

Before

source roles = [22, 13, [5, 32], [20, 47]]

After

derived = [[[5, 20, 25, 18], [5, 47, 52, 18], [32, 20, 39, 4], [32, 47, 12, 4]], [4, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S612

S614 · implies

Before

source roles = [22, 14, [5, 32], [21, 48]]

After

derived = [[[5, 21, 26, 19], [5, 48, 53, 19], [32, 21, 38, 3], [32, 48, 11, 3]], [3, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S613

S615 · implies

Before

source roles = [22, 15, [5, 32], [22, 49]]

After

derived = [[[5, 22, 0, 0], [5, 49, 27, 0], [32, 22, 37, 2], [32, 49, 10, 2]], [0, 2], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S614

S616 · implies

Before

source roles = [22, 16, [5, 32], [23, 50]]

After

derived = [[[5, 23, 1, 1], [5, 50, 28, 1], [32, 23, 36, 26], [32, 50, 9, 26]], [1, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S615

S617 · implies

Before

source roles = [22, 17, [5, 32], [24, 51]]

After

derived = [[[5, 24, 2, 12], [5, 51, 29, 12], [32, 24, 35, 25], [32, 51, 8, 25]], [12, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S616

S618 · implies

Before

source roles = [22, 18, [5, 32], [25, 52]]

After

derived = [[[5, 25, 3, 20], [5, 52, 30, 20], [32, 25, 34, 24], [32, 52, 7, 24]], [20, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S617

S619 · implies

Before

source roles = [22, 19, [5, 32], [26, 53]]

After

derived = [[[5, 26, 4, 21], [5, 53, 31, 21], [32, 26, 33, 23], [32, 53, 6, 23]], [21, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S618

S620 · implies

Before

source roles = [22, 20, [5, 32], [3, 30]]

After

derived = [[[5, 3, 8, 25], [5, 30, 35, 25], [32, 3, 29, 12], [32, 30, 2, 12]], [12, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S619

S621 · implies

Before

source roles = [22, 21, [5, 32], [4, 31]]

After

derived = [[[5, 4, 9, 26], [5, 31, 36, 26], [32, 4, 28, 1], [32, 31, 1, 1]], [1, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S620

S622 · implies

Before

source roles = [22, 22, [5, 32], [5, 32]]

After

derived = [[[5, 5, 10, 2], [5, 32, 37, 2], [32, 5, 27, 0], [32, 32, 0, 0]], [0, 2], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S621

S623 · implies

Before

source roles = [22, 23, [5, 32], [6, 33]]

After

derived = [[[5, 6, 11, 3], [5, 33, 38, 3], [32, 6, 53, 19], [32, 33, 26, 19]], [3, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S622

S624 · implies

Before

source roles = [22, 24, [5, 32], [7, 34]]

After

derived = [[[5, 7, 12, 4], [5, 34, 39, 4], [32, 7, 52, 18], [32, 34, 25, 18]], [4, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S623

S625 · implies

Before

source roles = [22, 25, [5, 32], [8, 35]]

After

derived = [[[5, 8, 13, 5], [5, 35, 40, 5], [32, 8, 51, 17], [32, 35, 24, 17]], [5, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S624

S626 · implies

Before

source roles = [22, 26, [5, 32], [9, 36]]

After

derived = [[[5, 9, 14, 6], [5, 36, 41, 6], [32, 9, 50, 16], [32, 36, 23, 16]], [6, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S625

S627 · implies

Before

source roles = [23, 0, [6, 33], [0, 27]]

After

derived = [[[6, 0, 6, 23], [6, 27, 33, 23], [33, 0, 33, 23], [33, 27, 6, 23]], [23], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S626

S628 · implies

Before

source roles = [23, 1, [6, 33], [1, 28]]

After

derived = [[[6, 1, 7, 24], [6, 28, 34, 24], [33, 1, 32, 22], [33, 28, 5, 22]], [22, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S627

S629 · implies

Before

source roles = [23, 2, [6, 33], [10, 37]]

After

derived = [[[6, 10, 16, 8], [6, 37, 43, 8], [33, 10, 50, 16], [33, 37, 23, 16]], [8, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S628

S630 · implies

Before

source roles = [23, 3, [6, 33], [11, 38]]

After

derived = [[[6, 11, 17, 9], [6, 38, 44, 9], [33, 11, 49, 15], [33, 38, 22, 15]], [9, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S629

S631 · implies

Before

source roles = [23, 4, [6, 33], [12, 39]]

After

derived = [[[6, 12, 18, 10], [6, 39, 45, 10], [33, 12, 48, 14], [33, 39, 21, 14]], [10, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S630

S632 · implies

Before

source roles = [23, 5, [6, 33], [13, 40]]

After

derived = [[[6, 13, 19, 11], [6, 40, 46, 11], [33, 13, 47, 13], [33, 40, 20, 13]], [11, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S631

S633 · implies

Before

source roles = [23, 6, [6, 33], [14, 41]]

After

derived = [[[6, 14, 20, 13], [6, 41, 47, 13], [33, 14, 46, 11], [33, 41, 19, 11]], [11, 13], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S632

S634 · implies

Before

source roles = [23, 7, [6, 33], [15, 42]]

After

derived = [[[6, 15, 21, 14], [6, 42, 48, 14], [33, 15, 45, 10], [33, 42, 18, 10]], [10, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S633

S635 · implies

Before

source roles = [23, 8, [6, 33], [16, 43]]

After

derived = [[[6, 16, 22, 15], [6, 43, 49, 15], [33, 16, 44, 9], [33, 43, 17, 9]], [9, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S634

S636 · implies

Before

source roles = [23, 9, [6, 33], [17, 44]]

After

derived = [[[6, 17, 23, 16], [6, 44, 50, 16], [33, 17, 43, 8], [33, 44, 16, 8]], [8, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S635

S637 · implies

Before

source roles = [23, 10, [6, 33], [18, 45]]

After

derived = [[[6, 18, 24, 17], [6, 45, 51, 17], [33, 18, 42, 7], [33, 45, 15, 7]], [7, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S636

S638 · implies

Before

source roles = [23, 11, [6, 33], [19, 46]]

After

derived = [[[6, 19, 25, 18], [6, 46, 52, 18], [33, 19, 41, 6], [33, 46, 14, 6]], [6, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S637

S639 · implies

Before

source roles = [23, 12, [6, 33], [2, 29]]

After

derived = [[[6, 2, 8, 25], [6, 29, 35, 25], [33, 2, 31, 21], [33, 29, 4, 21]], [21, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S638

S640 · implies

Before

source roles = [23, 13, [6, 33], [20, 47]]

After

derived = [[[6, 20, 26, 19], [6, 47, 53, 19], [33, 20, 40, 5], [33, 47, 13, 5]], [5, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S639

S641 · implies

Before

source roles = [23, 14, [6, 33], [21, 48]]

After

derived = [[[6, 21, 0, 0], [6, 48, 27, 0], [33, 21, 39, 4], [33, 48, 12, 4]], [0, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S640

S642 · implies

Before

source roles = [23, 15, [6, 33], [22, 49]]

After

derived = [[[6, 22, 1, 1], [6, 49, 28, 1], [33, 22, 38, 3], [33, 49, 11, 3]], [1, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S641

S643 · implies

Before

source roles = [23, 16, [6, 33], [23, 50]]

After

derived = [[[6, 23, 2, 12], [6, 50, 29, 12], [33, 23, 37, 2], [33, 50, 10, 2]], [2, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S642

S644 · implies

Before

source roles = [23, 17, [6, 33], [24, 51]]

After

derived = [[[6, 24, 3, 20], [6, 51, 30, 20], [33, 24, 36, 26], [33, 51, 9, 26]], [20, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S643

S645 · implies

Before

source roles = [23, 18, [6, 33], [25, 52]]

After

derived = [[[6, 25, 4, 21], [6, 52, 31, 21], [33, 25, 35, 25], [33, 52, 8, 25]], [21, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S644

S646 · implies

Before

source roles = [23, 19, [6, 33], [26, 53]]

After

derived = [[[6, 26, 5, 22], [6, 53, 32, 22], [33, 26, 34, 24], [33, 53, 7, 24]], [22, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S645

S647 · implies

Before

source roles = [23, 20, [6, 33], [3, 30]]

After

derived = [[[6, 3, 9, 26], [6, 30, 36, 26], [33, 3, 30, 20], [33, 30, 3, 20]], [20, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S646

S648 · implies

Before

source roles = [23, 21, [6, 33], [4, 31]]

After

derived = [[[6, 4, 10, 2], [6, 31, 37, 2], [33, 4, 29, 12], [33, 31, 2, 12]], [2, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S647

S649 · implies

Before

source roles = [23, 22, [6, 33], [5, 32]]

After

derived = [[[6, 5, 11, 3], [6, 32, 38, 3], [33, 5, 28, 1], [33, 32, 1, 1]], [1, 3], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S648

S650 · implies

Before

source roles = [23, 23, [6, 33], [6, 33]]

After

derived = [[[6, 6, 12, 4], [6, 33, 39, 4], [33, 6, 27, 0], [33, 33, 0, 0]], [0, 4], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S649

S651 · implies

Before

source roles = [23, 24, [6, 33], [7, 34]]

After

derived = [[[6, 7, 13, 5], [6, 34, 40, 5], [33, 7, 53, 19], [33, 34, 26, 19]], [5, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S650

S652 · implies

Before

source roles = [23, 25, [6, 33], [8, 35]]

After

derived = [[[6, 8, 14, 6], [6, 35, 41, 6], [33, 8, 52, 18], [33, 35, 25, 18]], [6, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S651

S653 · implies

Before

source roles = [23, 26, [6, 33], [9, 36]]

After

derived = [[[6, 9, 15, 7], [6, 36, 42, 7], [33, 9, 51, 17], [33, 36, 24, 17]], [7, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S652

S654 · implies

Before

source roles = [24, 0, [7, 34], [0, 27]]

After

derived = [[[7, 0, 7, 24], [7, 27, 34, 24], [34, 0, 34, 24], [34, 27, 7, 24]], [24], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S653

S655 · implies

Before

source roles = [24, 1, [7, 34], [1, 28]]

After

derived = [[[7, 1, 8, 25], [7, 28, 35, 25], [34, 1, 33, 23], [34, 28, 6, 23]], [23, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S654

S656 · implies

Before

source roles = [24, 2, [7, 34], [10, 37]]

After

derived = [[[7, 10, 17, 9], [7, 37, 44, 9], [34, 10, 51, 17], [34, 37, 24, 17]], [9, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S655

S657 · implies

Before

source roles = [24, 3, [7, 34], [11, 38]]

After

derived = [[[7, 11, 18, 10], [7, 38, 45, 10], [34, 11, 50, 16], [34, 38, 23, 16]], [10, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S656

S658 · implies

Before

source roles = [24, 4, [7, 34], [12, 39]]

After

derived = [[[7, 12, 19, 11], [7, 39, 46, 11], [34, 12, 49, 15], [34, 39, 22, 15]], [11, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S657

S659 · implies

Before

source roles = [24, 5, [7, 34], [13, 40]]

After

derived = [[[7, 13, 20, 13], [7, 40, 47, 13], [34, 13, 48, 14], [34, 40, 21, 14]], [13, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S658

S660 · implies

Before

source roles = [24, 6, [7, 34], [14, 41]]

After

derived = [[[7, 14, 21, 14], [7, 41, 48, 14], [34, 14, 47, 13], [34, 41, 20, 13]], [13, 14], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S659

S661 · implies

Before

source roles = [24, 7, [7, 34], [15, 42]]

After

derived = [[[7, 15, 22, 15], [7, 42, 49, 15], [34, 15, 46, 11], [34, 42, 19, 11]], [11, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S660

S662 · implies

Before

source roles = [24, 8, [7, 34], [16, 43]]

After

derived = [[[7, 16, 23, 16], [7, 43, 50, 16], [34, 16, 45, 10], [34, 43, 18, 10]], [10, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S661

S663 · implies

Before

source roles = [24, 9, [7, 34], [17, 44]]

After

derived = [[[7, 17, 24, 17], [7, 44, 51, 17], [34, 17, 44, 9], [34, 44, 17, 9]], [9, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S662

S664 · implies

Before

source roles = [24, 10, [7, 34], [18, 45]]

After

derived = [[[7, 18, 25, 18], [7, 45, 52, 18], [34, 18, 43, 8], [34, 45, 16, 8]], [8, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S663

S665 · implies

Before

source roles = [24, 11, [7, 34], [19, 46]]

After

derived = [[[7, 19, 26, 19], [7, 46, 53, 19], [34, 19, 42, 7], [34, 46, 15, 7]], [7, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S664

S666 · implies

Before

source roles = [24, 12, [7, 34], [2, 29]]

After

derived = [[[7, 2, 9, 26], [7, 29, 36, 26], [34, 2, 32, 22], [34, 29, 5, 22]], [22, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S665

S667 · implies

Before

source roles = [24, 13, [7, 34], [20, 47]]

After

derived = [[[7, 20, 0, 0], [7, 47, 27, 0], [34, 20, 41, 6], [34, 47, 14, 6]], [0, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S666

S668 · implies

Before

source roles = [24, 14, [7, 34], [21, 48]]

After

derived = [[[7, 21, 1, 1], [7, 48, 28, 1], [34, 21, 40, 5], [34, 48, 13, 5]], [1, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S667

S669 · implies

Before

source roles = [24, 15, [7, 34], [22, 49]]

After

derived = [[[7, 22, 2, 12], [7, 49, 29, 12], [34, 22, 39, 4], [34, 49, 12, 4]], [4, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S668

S670 · implies

Before

source roles = [24, 16, [7, 34], [23, 50]]

After

derived = [[[7, 23, 3, 20], [7, 50, 30, 20], [34, 23, 38, 3], [34, 50, 11, 3]], [3, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S669

S671 · implies

Before

source roles = [24, 17, [7, 34], [24, 51]]

After

derived = [[[7, 24, 4, 21], [7, 51, 31, 21], [34, 24, 37, 2], [34, 51, 10, 2]], [2, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S670

S672 · implies

Before

source roles = [24, 18, [7, 34], [25, 52]]

After

derived = [[[7, 25, 5, 22], [7, 52, 32, 22], [34, 25, 36, 26], [34, 52, 9, 26]], [22, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S671

S673 · implies

Before

source roles = [24, 19, [7, 34], [26, 53]]

After

derived = [[[7, 26, 6, 23], [7, 53, 33, 23], [34, 26, 35, 25], [34, 53, 8, 25]], [23, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S672

S674 · implies

Before

source roles = [24, 20, [7, 34], [3, 30]]

After

derived = [[[7, 3, 10, 2], [7, 30, 37, 2], [34, 3, 31, 21], [34, 30, 4, 21]], [2, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S673

S675 · implies

Before

source roles = [24, 21, [7, 34], [4, 31]]

After

derived = [[[7, 4, 11, 3], [7, 31, 38, 3], [34, 4, 30, 20], [34, 31, 3, 20]], [3, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S674

S676 · implies

Before

source roles = [24, 22, [7, 34], [5, 32]]

After

derived = [[[7, 5, 12, 4], [7, 32, 39, 4], [34, 5, 29, 12], [34, 32, 2, 12]], [4, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S675

S677 · implies

Before

source roles = [24, 23, [7, 34], [6, 33]]

After

derived = [[[7, 6, 13, 5], [7, 33, 40, 5], [34, 6, 28, 1], [34, 33, 1, 1]], [1, 5], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S676

S678 · implies

Before

source roles = [24, 24, [7, 34], [7, 34]]

After

derived = [[[7, 7, 14, 6], [7, 34, 41, 6], [34, 7, 27, 0], [34, 34, 0, 0]], [0, 6], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S677

S679 · implies

Before

source roles = [24, 25, [7, 34], [8, 35]]

After

derived = [[[7, 8, 15, 7], [7, 35, 42, 7], [34, 8, 53, 19], [34, 35, 26, 19]], [7, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S678

S680 · implies

Before

source roles = [24, 26, [7, 34], [9, 36]]

After

derived = [[[7, 9, 16, 8], [7, 36, 43, 8], [34, 9, 52, 18], [34, 36, 25, 18]], [8, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S679

S681 · implies

Before

source roles = [25, 0, [8, 35], [0, 27]]

After

derived = [[[8, 0, 8, 25], [8, 27, 35, 25], [35, 0, 35, 25], [35, 27, 8, 25]], [25], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S680

S682 · implies

Before

source roles = [25, 1, [8, 35], [1, 28]]

After

derived = [[[8, 1, 9, 26], [8, 28, 36, 26], [35, 1, 34, 24], [35, 28, 7, 24]], [24, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S681

S683 · implies

Before

source roles = [25, 2, [8, 35], [10, 37]]

After

derived = [[[8, 10, 18, 10], [8, 37, 45, 10], [35, 10, 52, 18], [35, 37, 25, 18]], [10, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S682

S684 · implies

Before

source roles = [25, 3, [8, 35], [11, 38]]

After

derived = [[[8, 11, 19, 11], [8, 38, 46, 11], [35, 11, 51, 17], [35, 38, 24, 17]], [11, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S683

S685 · implies

Before

source roles = [25, 4, [8, 35], [12, 39]]

After

derived = [[[8, 12, 20, 13], [8, 39, 47, 13], [35, 12, 50, 16], [35, 39, 23, 16]], [13, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S684

S686 · implies

Before

source roles = [25, 5, [8, 35], [13, 40]]

After

derived = [[[8, 13, 21, 14], [8, 40, 48, 14], [35, 13, 49, 15], [35, 40, 22, 15]], [14, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S685

S687 · implies

Before

source roles = [25, 6, [8, 35], [14, 41]]

After

derived = [[[8, 14, 22, 15], [8, 41, 49, 15], [35, 14, 48, 14], [35, 41, 21, 14]], [14, 15], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S686

S688 · implies

Before

source roles = [25, 7, [8, 35], [15, 42]]

After

derived = [[[8, 15, 23, 16], [8, 42, 50, 16], [35, 15, 47, 13], [35, 42, 20, 13]], [13, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S687

S689 · implies

Before

source roles = [25, 8, [8, 35], [16, 43]]

After

derived = [[[8, 16, 24, 17], [8, 43, 51, 17], [35, 16, 46, 11], [35, 43, 19, 11]], [11, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S688

S690 · implies

Before

source roles = [25, 9, [8, 35], [17, 44]]

After

derived = [[[8, 17, 25, 18], [8, 44, 52, 18], [35, 17, 45, 10], [35, 44, 18, 10]], [10, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S689

S691 · implies

Before

source roles = [25, 10, [8, 35], [18, 45]]

After

derived = [[[8, 18, 26, 19], [8, 45, 53, 19], [35, 18, 44, 9], [35, 45, 17, 9]], [9, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S690

S692 · implies

Before

source roles = [25, 11, [8, 35], [19, 46]]

After

derived = [[[8, 19, 0, 0], [8, 46, 27, 0], [35, 19, 43, 8], [35, 46, 16, 8]], [0, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S691

S693 · implies

Before

source roles = [25, 12, [8, 35], [2, 29]]

After

derived = [[[8, 2, 10, 2], [8, 29, 37, 2], [35, 2, 33, 23], [35, 29, 6, 23]], [2, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S692

S694 · implies

Before

source roles = [25, 13, [8, 35], [20, 47]]

After

derived = [[[8, 20, 1, 1], [8, 47, 28, 1], [35, 20, 42, 7], [35, 47, 15, 7]], [1, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S693

S695 · implies

Before

source roles = [25, 14, [8, 35], [21, 48]]

After

derived = [[[8, 21, 2, 12], [8, 48, 29, 12], [35, 21, 41, 6], [35, 48, 14, 6]], [6, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S694

S696 · implies

Before

source roles = [25, 15, [8, 35], [22, 49]]

After

derived = [[[8, 22, 3, 20], [8, 49, 30, 20], [35, 22, 40, 5], [35, 49, 13, 5]], [5, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S695

S697 · implies

Before

source roles = [25, 16, [8, 35], [23, 50]]

After

derived = [[[8, 23, 4, 21], [8, 50, 31, 21], [35, 23, 39, 4], [35, 50, 12, 4]], [4, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S696

S698 · implies

Before

source roles = [25, 17, [8, 35], [24, 51]]

After

derived = [[[8, 24, 5, 22], [8, 51, 32, 22], [35, 24, 38, 3], [35, 51, 11, 3]], [3, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S697

S699 · implies

Before

source roles = [25, 18, [8, 35], [25, 52]]

After

derived = [[[8, 25, 6, 23], [8, 52, 33, 23], [35, 25, 37, 2], [35, 52, 10, 2]], [2, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S698

S700 · implies

Before

source roles = [25, 19, [8, 35], [26, 53]]

After

derived = [[[8, 26, 7, 24], [8, 53, 34, 24], [35, 26, 36, 26], [35, 53, 9, 26]], [24, 26], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S699

S701 · implies

Before

source roles = [25, 20, [8, 35], [3, 30]]

After

derived = [[[8, 3, 11, 3], [8, 30, 38, 3], [35, 3, 32, 22], [35, 30, 5, 22]], [3, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S700

S702 · implies

Before

source roles = [25, 21, [8, 35], [4, 31]]

After

derived = [[[8, 4, 12, 4], [8, 31, 39, 4], [35, 4, 31, 21], [35, 31, 4, 21]], [4, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S701

S703 · implies

Before

source roles = [25, 22, [8, 35], [5, 32]]

After

derived = [[[8, 5, 13, 5], [8, 32, 40, 5], [35, 5, 30, 20], [35, 32, 3, 20]], [5, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S702

S704 · implies

Before

source roles = [25, 23, [8, 35], [6, 33]]

After

derived = [[[8, 6, 14, 6], [8, 33, 41, 6], [35, 6, 29, 12], [35, 33, 2, 12]], [6, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S703

S705 · implies

Before

source roles = [25, 24, [8, 35], [7, 34]]

After

derived = [[[8, 7, 15, 7], [8, 34, 42, 7], [35, 7, 28, 1], [35, 34, 1, 1]], [1, 7], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S704

S706 · implies

Before

source roles = [25, 25, [8, 35], [8, 35]]

After

derived = [[[8, 8, 16, 8], [8, 35, 43, 8], [35, 8, 27, 0], [35, 35, 0, 0]], [0, 8], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S705

S707 · implies

Before

source roles = [25, 26, [8, 35], [9, 36]]

After

derived = [[[8, 9, 17, 9], [8, 36, 44, 9], [35, 9, 53, 19], [35, 36, 26, 19]], [9, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S706

S708 · implies

Before

source roles = [26, 0, [9, 36], [0, 27]]

After

derived = [[[9, 0, 9, 26], [9, 27, 36, 26], [36, 0, 36, 26], [36, 27, 9, 26]], [26], Yes]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S707

S709 · implies

Before

source roles = [26, 1, [9, 36], [1, 28]]

After

derived = [[[9, 1, 10, 2], [9, 28, 37, 2], [36, 1, 35, 25], [36, 28, 8, 25]], [2, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S708

S710 · implies

Before

source roles = [26, 2, [9, 36], [10, 37]]

After

derived = [[[9, 10, 19, 11], [9, 37, 46, 11], [36, 10, 53, 19], [36, 37, 26, 19]], [11, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S709

S711 · implies

Before

source roles = [26, 3, [9, 36], [11, 38]]

After

derived = [[[9, 11, 20, 13], [9, 38, 47, 13], [36, 11, 52, 18], [36, 38, 25, 18]], [13, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S710

S712 · implies

Before

source roles = [26, 4, [9, 36], [12, 39]]

After

derived = [[[9, 12, 21, 14], [9, 39, 48, 14], [36, 12, 51, 17], [36, 39, 24, 17]], [14, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S711

S713 · implies

Before

source roles = [26, 5, [9, 36], [13, 40]]

After

derived = [[[9, 13, 22, 15], [9, 40, 49, 15], [36, 13, 50, 16], [36, 40, 23, 16]], [15, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S712

S714 · implies

Before

source roles = [26, 6, [9, 36], [14, 41]]

After

derived = [[[9, 14, 23, 16], [9, 41, 50, 16], [36, 14, 49, 15], [36, 41, 22, 15]], [15, 16], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S713

S715 · implies

Before

source roles = [26, 7, [9, 36], [15, 42]]

After

derived = [[[9, 15, 24, 17], [9, 42, 51, 17], [36, 15, 48, 14], [36, 42, 21, 14]], [14, 17], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S714

S716 · implies

Before

source roles = [26, 8, [9, 36], [16, 43]]

After

derived = [[[9, 16, 25, 18], [9, 43, 52, 18], [36, 16, 47, 13], [36, 43, 20, 13]], [13, 18], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S715

S717 · implies

Before

source roles = [26, 9, [9, 36], [17, 44]]

After

derived = [[[9, 17, 26, 19], [9, 44, 53, 19], [36, 17, 46, 11], [36, 44, 19, 11]], [11, 19], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S716

S718 · implies

Before

source roles = [26, 10, [9, 36], [18, 45]]

After

derived = [[[9, 18, 0, 0], [9, 45, 27, 0], [36, 18, 45, 10], [36, 45, 18, 10]], [0, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S717

S719 · implies

Before

source roles = [26, 11, [9, 36], [19, 46]]

After

derived = [[[9, 19, 1, 1], [9, 46, 28, 1], [36, 19, 44, 9], [36, 46, 17, 9]], [1, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S718

S720 · implies

Before

source roles = [26, 12, [9, 36], [2, 29]]

After

derived = [[[9, 2, 11, 3], [9, 29, 38, 3], [36, 2, 34, 24], [36, 29, 7, 24]], [3, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S719

S721 · implies

Before

source roles = [26, 13, [9, 36], [20, 47]]

After

derived = [[[9, 20, 2, 12], [9, 47, 29, 12], [36, 20, 43, 8], [36, 47, 16, 8]], [8, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S720

S722 · implies

Before

source roles = [26, 14, [9, 36], [21, 48]]

After

derived = [[[9, 21, 3, 20], [9, 48, 30, 20], [36, 21, 42, 7], [36, 48, 15, 7]], [7, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S721

S723 · implies

Before

source roles = [26, 15, [9, 36], [22, 49]]

After

derived = [[[9, 22, 4, 21], [9, 49, 31, 21], [36, 22, 41, 6], [36, 49, 14, 6]], [6, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S722

S724 · implies

Before

source roles = [26, 16, [9, 36], [23, 50]]

After

derived = [[[9, 23, 5, 22], [9, 50, 32, 22], [36, 23, 40, 5], [36, 50, 13, 5]], [5, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S723

S725 · implies

Before

source roles = [26, 17, [9, 36], [24, 51]]

After

derived = [[[9, 24, 6, 23], [9, 51, 33, 23], [36, 24, 39, 4], [36, 51, 12, 4]], [4, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S724

S726 · implies

Before

source roles = [26, 18, [9, 36], [25, 52]]

After

derived = [[[9, 25, 7, 24], [9, 52, 34, 24], [36, 25, 38, 3], [36, 52, 11, 3]], [3, 24], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S725

S727 · implies

Before

source roles = [26, 19, [9, 36], [26, 53]]

After

derived = [[[9, 26, 8, 25], [9, 53, 35, 25], [36, 26, 37, 2], [36, 53, 10, 2]], [2, 25], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S726

S728 · implies

Before

source roles = [26, 20, [9, 36], [3, 30]]

After

derived = [[[9, 3, 12, 4], [9, 30, 39, 4], [36, 3, 33, 23], [36, 30, 6, 23]], [4, 23], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S727

S729 · implies

Before

source roles = [26, 21, [9, 36], [4, 31]]

After

derived = [[[9, 4, 13, 5], [9, 31, 40, 5], [36, 4, 32, 22], [36, 31, 5, 22]], [5, 22], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S728

S730 · implies

Before

source roles = [26, 22, [9, 36], [5, 32]]

After

derived = [[[9, 5, 14, 6], [9, 32, 41, 6], [36, 5, 31, 21], [36, 32, 4, 21]], [6, 21], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S729

S731 · implies

Before

source roles = [26, 23, [9, 36], [6, 33]]

After

derived = [[[9, 6, 15, 7], [9, 33, 42, 7], [36, 6, 30, 20], [36, 33, 3, 20]], [7, 20], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S730

S732 · implies

Before

source roles = [26, 24, [9, 36], [7, 34]]

After

derived = [[[9, 7, 16, 8], [9, 34, 43, 8], [36, 7, 29, 12], [36, 34, 2, 12]], [8, 12], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S731

S733 · implies

Before

source roles = [26, 25, [9, 36], [8, 35]]

After

derived = [[[9, 8, 17, 9], [9, 35, 44, 9], [36, 8, 28, 1], [36, 35, 1, 1]], [1, 9], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S732

S734 · implies

Before

source roles = [26, 26, [9, 36], [9, 36]]

After

derived = [[[9, 9, 18, 10], [9, 36, 45, 10], [36, 9, 27, 0], [36, 36, 0, 0]], [0, 10], No]

Conditions: none

Step identifiers and dependencies

Rule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S733

S735 · implies

Before

source roles = [[0, 1, [1, 19], No], [0, 27], [1, 28]]

After

derived = [[0, 1, 0, 1, 1, 27, 1, 19], No, No]

Conditions: none

Keep the source first bad ordered pair and left,left2,right,right2 search order.Different representatives of the same two cosets give different product cosets,so multiplication fails to be well-defined.The subgroup and coset partition remain valid;do not invent a quotient table.

Step identifiers and dependencies

Rule: Quotient_FIRST_bad_pair_exact_source_nested_representative_witness · Uses: G001, S734

Reverse checks

S735 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S734 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S733 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S732 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S731 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S730 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S729 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S728 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S727 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S726 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S725 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S724 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S723 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S722 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S721 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S720 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S719 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S718 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S717 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S716 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S715 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S714 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S713 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S712 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S711 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S710 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S709 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S708 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S707 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S706 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S705 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S704 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S703 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S702 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S701 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S700 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S699 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S698 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S697 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S696 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S695 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S694 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S693 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S692 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S691 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S690 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S689 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S688 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S687 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S686 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S685 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S684 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S683 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S682 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S681 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S680 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S679 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S678 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S677 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S676 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S675 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S674 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S673 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S672 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S671 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S670 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S669 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S668 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S667 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S666 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S665 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S664 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S663 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S662 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S661 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S660 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S659 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S658 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S657 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S656 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S655 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S654 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S653 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S652 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S651 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S650 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S649 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S648 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S647 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S646 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S645 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S644 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S643 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S642 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S641 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S640 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S639 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S638 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S637 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S636 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S635 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S634 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S633 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S632 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S631 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S630 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S629 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S628 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S627 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S626 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S625 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S624 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S623 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S622 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S621 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S620 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S619 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S618 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S617 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S616 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S615 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S614 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S613 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S612 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S611 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S610 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S609 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S608 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S607 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S606 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S605 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S604 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S603 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S602 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S601 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S600 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S599 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S598 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S597 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S596 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S595 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S594 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S593 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S592 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S591 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S590 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S589 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S588 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S587 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S586 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S585 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S584 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S583 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S582 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S581 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S580 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S579 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S578 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S577 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S576 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S575 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S574 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S573 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S572 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S571 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S570 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S569 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S568 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S567 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S566 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S565 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S564 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S563 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S562 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S561 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S560 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S559 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S558 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S557 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S556 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S555 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S554 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S553 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S552 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S551 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S550 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S549 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S548 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S547 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S546 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S545 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S544 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S543 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S542 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S541 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S540 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S539 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S538 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S537 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S536 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S535 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S534 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S533 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S532 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S531 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S530 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S529 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S528 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S527 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S526 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S525 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S524 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S523 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S522 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S521 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S520 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S519 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S518 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S517 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S516 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S515 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S514 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S513 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S512 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S511 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S510 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S509 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S508 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S507 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S506 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S505 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S504 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S503 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S502 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S501 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S500 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S499 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S498 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S497 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S496 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S495 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S494 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S493 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S492 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S491 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S490 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S489 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S488 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S487 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S486 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S485 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S484 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S483 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S482 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S481 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S480 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S479 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S478 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S477 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S476 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S475 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S474 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S473 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S472 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S471 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S470 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S469 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S468 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S467 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S466 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S465 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S464 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S463 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S462 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S461 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S460 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S459 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S458 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S457 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S456 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S455 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S454 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S453 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S452 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S451 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S450 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S449 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S448 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S447 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S446 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S445 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S444 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S443 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S442 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S441 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S440 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S439 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S438 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S437 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S436 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S435 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S434 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S433 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S432 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S431 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S430 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S429 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S428 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S427 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S426 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S425 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S424 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S423 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S422 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S421 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S420 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S419 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S418 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S417 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S416 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S415 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S414 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S413 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S412 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S411 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S410 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S409 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S408 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S407 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S406 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S405 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S404 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S403 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S402 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S401 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S400 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S399 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S398 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S397 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S396 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S395 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S394 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S393 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S392 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S391 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S390 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S389 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S388 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S387 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S386 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S385 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S384 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S383 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S382 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S381 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S380 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S379 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S378 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S377 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S376 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S375 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S374 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S373 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S372 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S371 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S370 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S369 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S368 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S367 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S366 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S365 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S364 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S363 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S362 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S361 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S360 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S359 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S358 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S357 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S356 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S355 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S354 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S353 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S352 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S351 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S350 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S349 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S348 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S347 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S346 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S345 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S344 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S343 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S342 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S341 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S340 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S339 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S338 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S337 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S336 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S335 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S334 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S333 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S332 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S331 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S330 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S329 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S328 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S327 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S326 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S325 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S324 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S323 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S322 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S321 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S320 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S319 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S318 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S317 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S316 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S315 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S314 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S313 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S312 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S311 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S310 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S309 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S308 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S307 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S306 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S305 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S304 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S303 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S302 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S301 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S300 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S299 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S298 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S297 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S296 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S295 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S294 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S293 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S292 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S291 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S290 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S289 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S288 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S287 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S286 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S285 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S284 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S283 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S282 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S281 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S280 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S279 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S278 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S277 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S276 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S275 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S274 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S273 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S272 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S271 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S270 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S269 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S268 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S267 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S266 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S265 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S264 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S263 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S262 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S261 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S260 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S259 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S258 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S257 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S256 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S255 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S254 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S253 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S252 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S251 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S250 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S249 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S248 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S247 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S246 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S245 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S244 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S243 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S242 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S241 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S240 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S239 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S238 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S237 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S236 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S235 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S234 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S233 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S232 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S231 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S230 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S229 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S228 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S227 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S226 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S225 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S224 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S223 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S222 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S221 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S220 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S219 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S218 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S217 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S216 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S215 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S214 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S213 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S212 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S211 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S210 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S209 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S208 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S207 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S206 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S205 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S204 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S203 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S202 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S201 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S200 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S199 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S198 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S197 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S196 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S195 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S194 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S193 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S192 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S191 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S190 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S189 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S188 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S187 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S186 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S185 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S184 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S183 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S182 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S181 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S180 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S179 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S178 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S177 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S176 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S175 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S174 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S173 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S172 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S171 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S170 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S169 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S168 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S167 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S166 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S165 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S164 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S163 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S162 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S161 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S160 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S159 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S158 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S157 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S156 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S155 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S154 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S153 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S152 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S151 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S150 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S149 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S148 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S147 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S146 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S145 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S144 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S143 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S142 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S141 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S140 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S139 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S138 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S137 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S136 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S135 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S134 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S133 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S132 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S131 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S130 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S129 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S128 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S127 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S126 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S125 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S124 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S123 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S122 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S121 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S120 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S119 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S118 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S117 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S116 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S115 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S114 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S113 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S112 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S111 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S110 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S109 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S108 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S107 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S106 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S105 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S104 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S103 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S102 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S101 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S100 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S099 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S098 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S097 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S096 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S095 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S094 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S093 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S092 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S091 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S090 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S089 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S088 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S087 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S086 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S085 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S084 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S083 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S082 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S081 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S080 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S079 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S078 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S077 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S076 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S075 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S074 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S073 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S072 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S071 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S070 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S069 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S068 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S067 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S066 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S065 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S064 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S063 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S062 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S061 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S060 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S059 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S058 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S057 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S056 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S055 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S054 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S053 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S052 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S051 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S050 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S049 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S048 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S047 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S046 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S045 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S044 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S043 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S042 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S041 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S040 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S039 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S038 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S037 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S036 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S035 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S034 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S033 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S032 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S031 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S030 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S029 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S028 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S027 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S025 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S023 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S022 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S020 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S019 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S018 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S017 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S016 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S015 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([0, 27], No, [[0, 27], [1, 28], [10, 37], [11, 38], [12, 39], [13, 40], [14, 41], [15, 42], [16, 43], [17, 44], [18, 45], [19, 46], [2, 29], [20, 47], [21, 48], [22, 49], [23, 50], [24, 51], [25, 52], [26, 53], [3, 30], [4, 31], [5, 32], [6, 33], [7, 34], [8, 35], [9, 36]], [0, 1, 0, 1, 1, 27, 1, 19], No, No, explicit_representative_dependence_blocks_quotient_group_multiplication)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts

input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
original question SHA-256: 7cdf8a6f37e4569e706c02a4e03824e08cc4d66fa043d10bb99445132373dc05
candidate record SHA-256: 8bee5be39a183e67355665be83648de8d7bf1270cb894c18d964c5356da1b71e
semantic review receipt SHA-256: 6212b8b0b3b273f3a514e26ebd17d7e81219c56a8f47e40047ee2b6bf01d1ba3
question-first witness SHA-256: f32a23d5e1b66c7794c60def58741bcdfacff24f3cdfc9bc48109c8f71543cf3
Lean: NOT_RUN · human review: NOT_PERFORMED

Same-source full JSON