# Question 25346: Explicit Representative Dependence Blocks This Quotient Multiplication

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0049-25346 · q-20261015-advance-20261114-r02-finite-quotient-group-0096



## 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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21], [44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22], [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, 23] 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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15, 14], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16, 15], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17, 16], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18, 17], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19, 18], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20, 19], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21, 20], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22, 21], [44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 22], [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, 23] 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](https://ocme.evemisslab.com/en/mko/mko-finite-quotient-group/)





## Step-by-step derivation

S001 · impliesBefore

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 dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

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

Conditions: none

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

Step identifiers and dependenciesRule: Quotient_complete_group_table_actual_identity · Uses: G001, S001





S003 · impliesBefore

source roles = [46, 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]], 97336, [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]]

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 dependenciesRule: Quotient_ALL_group_associativity_triples_and_two_sided_inverses · Uses: G001, S002





S004 · impliesBefore

source roles = [0, [0, 23]]

After

derived = [[[0, 0, 0, Yes], [0, 23, 23, Yes], [23, 0, 23, Yes], [23, 23, 0, Yes]], [[0, 0, Yes], [23, 23, Yes]], Yes, [[0, [0, 23]], [1, [0, 25]], [2, [0, 27]], [3, [0, 29]], [4, [0, 31]], [5, [0, 33]], [6, [0, 35]], [7, [0, 37]], [8, [0, 39]], [9, [0, 41]], [10, [0, 43]], [11, [0, 45]], [12, [0, 24]], [13, [0, 26]], [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, 23]], [24, [0, 25]], [25, [0, 27]], [26, [0, 29]], [27, [0, 31]], [28, [0, 33]], [29, [0, 35]], [30, [0, 37]], [31, [0, 39]], [32, [0, 41]], [33, [0, 43]], [34, [0, 45]], [35, [0, 24]], [36, [0, 26]], [37, [0, 28]], [38, [0, 30]], [39, [0, 32]], [40, [0, 34]], [41, [0, 36]], [42, [0, 38]], [43, [0, 40]], [44, [0, 42]], [45, [0, 44]]], 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 dependenciesRule: Quotient_genuine_subgroup_before_actual_normality · Uses: G001, S003





S005 · impliesBefore

source roles = [[0, 23], [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]]

After

derived = [[[0, 23], [1, 24], [10, 33], [11, 34], [12, 35], [13, 36], [14, 37], [15, 38], [16, 39], [17, 40], [18, 41], [19, 42], [2, 25], [20, 43], [21, 44], [22, 45], [3, 26], [4, 27], [5, 28], [6, 29], [7, 30], [8, 31], [9, 32]], [0, 1, 12, 16, 17, 18, 19, 20, 21, 22, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 0, 1, 12, 16, 17, 18, 19, 20, 21, 22, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15], 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 dependenciesRule: Quotient_ALL_LEFT_coset_SETS_complete_disjoint_partition · Uses: G001, S004





S006 · impliesBefore

source roles = [0, 0, [0, 23], [0, 23]]

After

derived = [[[0, 0, 0, 0], [0, 23, 23, 0], [23, 0, 23, 0], [23, 23, 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S005





S007 · impliesBefore

source roles = [0, 1, [0, 23], [1, 24]]

After

derived = [[[0, 1, 1, 1], [0, 24, 24, 1], [23, 1, 45, 15], [23, 24, 22, 15]], [1, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S006





S008 · impliesBefore

source roles = [0, 2, [0, 23], [10, 33]]

After

derived = [[[0, 10, 10, 2], [0, 33, 33, 2], [23, 10, 36, 5], [23, 33, 13, 5]], [2, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S007





S009 · impliesBefore

source roles = [0, 3, [0, 23], [11, 34]]

After

derived = [[[0, 11, 11, 3], [0, 34, 34, 3], [23, 11, 35, 4], [23, 34, 12, 4]], [3, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S008





S010 · impliesBefore

source roles = [0, 4, [0, 23], [12, 35]]

After

derived = [[[0, 12, 12, 4], [0, 35, 35, 4], [23, 12, 34, 3], [23, 35, 11, 3]], [3, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S009





S011 · impliesBefore

source roles = [0, 5, [0, 23], [13, 36]]

After

derived = [[[0, 13, 13, 5], [0, 36, 36, 5], [23, 13, 33, 2], [23, 36, 10, 2]], [2, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S010





S012 · impliesBefore

source roles = [0, 6, [0, 23], [14, 37]]

After

derived = [[[0, 14, 14, 6], [0, 37, 37, 6], [23, 14, 32, 22], [23, 37, 9, 22]], [6, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S011





S013 · impliesBefore

source roles = [0, 7, [0, 23], [15, 38]]

After

derived = [[[0, 15, 15, 7], [0, 38, 38, 7], [23, 15, 31, 21], [23, 38, 8, 21]], [7, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S012





S014 · impliesBefore

source roles = [0, 8, [0, 23], [16, 39]]

After

derived = [[[0, 16, 16, 8], [0, 39, 39, 8], [23, 16, 30, 20], [23, 39, 7, 20]], [8, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S013





S015 · impliesBefore

source roles = [0, 9, [0, 23], [17, 40]]

After

derived = [[[0, 17, 17, 9], [0, 40, 40, 9], [23, 17, 29, 19], [23, 40, 6, 19]], [9, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S014





S016 · impliesBefore

source roles = [0, 10, [0, 23], [18, 41]]

After

derived = [[[0, 18, 18, 10], [0, 41, 41, 10], [23, 18, 28, 18], [23, 41, 5, 18]], [10, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S015





S017 · impliesBefore

source roles = [0, 11, [0, 23], [19, 42]]

After

derived = [[[0, 19, 19, 11], [0, 42, 42, 11], [23, 19, 27, 17], [23, 42, 4, 17]], [11, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S016





S018 · impliesBefore

source roles = [0, 12, [0, 23], [2, 25]]

After

derived = [[[0, 2, 2, 12], [0, 25, 25, 12], [23, 2, 44, 14], [23, 25, 21, 14]], [12, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S017





S019 · impliesBefore

source roles = [0, 13, [0, 23], [20, 43]]

After

derived = [[[0, 20, 20, 13], [0, 43, 43, 13], [23, 20, 26, 16], [23, 43, 3, 16]], [13, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S018





S020 · impliesBefore

source roles = [0, 14, [0, 23], [21, 44]]

After

derived = [[[0, 21, 21, 14], [0, 44, 44, 14], [23, 21, 25, 12], [23, 44, 2, 12]], [12, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S019





S021 · impliesBefore

source roles = [0, 15, [0, 23], [22, 45]]

After

derived = [[[0, 22, 22, 15], [0, 45, 45, 15], [23, 22, 24, 1], [23, 45, 1, 1]], [1, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S020





S022 · impliesBefore

source roles = [0, 16, [0, 23], [3, 26]]

After

derived = [[[0, 3, 3, 16], [0, 26, 26, 16], [23, 3, 43, 13], [23, 26, 20, 13]], [13, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S021





S023 · impliesBefore

source roles = [0, 17, [0, 23], [4, 27]]

After

derived = [[[0, 4, 4, 17], [0, 27, 27, 17], [23, 4, 42, 11], [23, 27, 19, 11]], [11, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S022





S024 · impliesBefore

source roles = [0, 18, [0, 23], [5, 28]]

After

derived = [[[0, 5, 5, 18], [0, 28, 28, 18], [23, 5, 41, 10], [23, 28, 18, 10]], [10, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S023





S025 · impliesBefore

source roles = [0, 19, [0, 23], [6, 29]]

After

derived = [[[0, 6, 6, 19], [0, 29, 29, 19], [23, 6, 40, 9], [23, 29, 17, 9]], [9, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S024





S026 · impliesBefore

source roles = [0, 20, [0, 23], [7, 30]]

After

derived = [[[0, 7, 7, 20], [0, 30, 30, 20], [23, 7, 39, 8], [23, 30, 16, 8]], [8, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S025





S027 · impliesBefore

source roles = [0, 21, [0, 23], [8, 31]]

After

derived = [[[0, 8, 8, 21], [0, 31, 31, 21], [23, 8, 38, 7], [23, 31, 15, 7]], [7, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S026





S028 · impliesBefore

source roles = [0, 22, [0, 23], [9, 32]]

After

derived = [[[0, 9, 9, 22], [0, 32, 32, 22], [23, 9, 37, 6], [23, 32, 14, 6]], [6, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S027





S029 · impliesBefore

source roles = [1, 0, [1, 24], [0, 23]]

After

derived = [[[1, 0, 1, 1], [1, 23, 24, 1], [24, 0, 24, 1], [24, 23, 1, 1]], [1], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S028





S030 · impliesBefore

source roles = [1, 1, [1, 24], [1, 24]]

After

derived = [[[1, 1, 2, 12], [1, 24, 25, 12], [24, 1, 23, 0], [24, 24, 0, 0]], [0, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S029





S031 · impliesBefore

source roles = [1, 2, [1, 24], [10, 33]]

After

derived = [[[1, 10, 11, 3], [1, 33, 34, 3], [24, 10, 37, 6], [24, 33, 14, 6]], [3, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S030





S032 · impliesBefore

source roles = [1, 3, [1, 24], [11, 34]]

After

derived = [[[1, 11, 12, 4], [1, 34, 35, 4], [24, 11, 36, 5], [24, 34, 13, 5]], [4, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S031





S033 · impliesBefore

source roles = [1, 4, [1, 24], [12, 35]]

After

derived = [[[1, 12, 13, 5], [1, 35, 36, 5], [24, 12, 35, 4], [24, 35, 12, 4]], [4, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S032





S034 · impliesBefore

source roles = [1, 5, [1, 24], [13, 36]]

After

derived = [[[1, 13, 14, 6], [1, 36, 37, 6], [24, 13, 34, 3], [24, 36, 11, 3]], [3, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S033





S035 · impliesBefore

source roles = [1, 6, [1, 24], [14, 37]]

After

derived = [[[1, 14, 15, 7], [1, 37, 38, 7], [24, 14, 33, 2], [24, 37, 10, 2]], [2, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S034





S036 · impliesBefore

source roles = [1, 7, [1, 24], [15, 38]]

After

derived = [[[1, 15, 16, 8], [1, 38, 39, 8], [24, 15, 32, 22], [24, 38, 9, 22]], [8, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S035





S037 · impliesBefore

source roles = [1, 8, [1, 24], [16, 39]]

After

derived = [[[1, 16, 17, 9], [1, 39, 40, 9], [24, 16, 31, 21], [24, 39, 8, 21]], [9, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S036





S038 · impliesBefore

source roles = [1, 9, [1, 24], [17, 40]]

After

derived = [[[1, 17, 18, 10], [1, 40, 41, 10], [24, 17, 30, 20], [24, 40, 7, 20]], [10, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S037





S039 · impliesBefore

source roles = [1, 10, [1, 24], [18, 41]]

After

derived = [[[1, 18, 19, 11], [1, 41, 42, 11], [24, 18, 29, 19], [24, 41, 6, 19]], [11, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S038





S040 · impliesBefore

source roles = [1, 11, [1, 24], [19, 42]]

After

derived = [[[1, 19, 20, 13], [1, 42, 43, 13], [24, 19, 28, 18], [24, 42, 5, 18]], [13, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S039





S041 · impliesBefore

source roles = [1, 12, [1, 24], [2, 25]]

After

derived = [[[1, 2, 3, 16], [1, 25, 26, 16], [24, 2, 45, 15], [24, 25, 22, 15]], [15, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S040





S042 · impliesBefore

source roles = [1, 13, [1, 24], [20, 43]]

After

derived = [[[1, 20, 21, 14], [1, 43, 44, 14], [24, 20, 27, 17], [24, 43, 4, 17]], [14, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S041





S043 · impliesBefore

source roles = [1, 14, [1, 24], [21, 44]]

After

derived = [[[1, 21, 22, 15], [1, 44, 45, 15], [24, 21, 26, 16], [24, 44, 3, 16]], [15, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S042





S044 · impliesBefore

source roles = [1, 15, [1, 24], [22, 45]]

After

derived = [[[1, 22, 0, 0], [1, 45, 23, 0], [24, 22, 25, 12], [24, 45, 2, 12]], [0, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S043





S045 · impliesBefore

source roles = [1, 16, [1, 24], [3, 26]]

After

derived = [[[1, 3, 4, 17], [1, 26, 27, 17], [24, 3, 44, 14], [24, 26, 21, 14]], [14, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S044





S046 · impliesBefore

source roles = [1, 17, [1, 24], [4, 27]]

After

derived = [[[1, 4, 5, 18], [1, 27, 28, 18], [24, 4, 43, 13], [24, 27, 20, 13]], [13, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S045





S047 · impliesBefore

source roles = [1, 18, [1, 24], [5, 28]]

After

derived = [[[1, 5, 6, 19], [1, 28, 29, 19], [24, 5, 42, 11], [24, 28, 19, 11]], [11, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S046





S048 · impliesBefore

source roles = [1, 19, [1, 24], [6, 29]]

After

derived = [[[1, 6, 7, 20], [1, 29, 30, 20], [24, 6, 41, 10], [24, 29, 18, 10]], [10, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S047





S049 · impliesBefore

source roles = [1, 20, [1, 24], [7, 30]]

After

derived = [[[1, 7, 8, 21], [1, 30, 31, 21], [24, 7, 40, 9], [24, 30, 17, 9]], [9, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S048





S050 · impliesBefore

source roles = [1, 21, [1, 24], [8, 31]]

After

derived = [[[1, 8, 9, 22], [1, 31, 32, 22], [24, 8, 39, 8], [24, 31, 16, 8]], [8, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S049





S051 · impliesBefore

source roles = [1, 22, [1, 24], [9, 32]]

After

derived = [[[1, 9, 10, 2], [1, 32, 33, 2], [24, 9, 38, 7], [24, 32, 15, 7]], [2, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S050





S052 · impliesBefore

source roles = [2, 0, [10, 33], [0, 23]]

After

derived = [[[10, 0, 10, 2], [10, 23, 33, 2], [33, 0, 33, 2], [33, 23, 10, 2]], [2], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S051





S053 · impliesBefore

source roles = [2, 1, [10, 33], [1, 24]]

After

derived = [[[10, 1, 11, 3], [10, 24, 34, 3], [33, 1, 32, 22], [33, 24, 9, 22]], [3, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S052





S054 · impliesBefore

source roles = [2, 2, [10, 33], [10, 33]]

After

derived = [[[10, 10, 20, 13], [10, 33, 43, 13], [33, 10, 23, 0], [33, 33, 0, 0]], [0, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S053





S055 · impliesBefore

source roles = [2, 3, [10, 33], [11, 34]]

After

derived = [[[10, 11, 21, 14], [10, 34, 44, 14], [33, 11, 45, 15], [33, 34, 22, 15]], [14, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S054





S056 · impliesBefore

source roles = [2, 4, [10, 33], [12, 35]]

After

derived = [[[10, 12, 22, 15], [10, 35, 45, 15], [33, 12, 44, 14], [33, 35, 21, 14]], [14, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S055





S057 · impliesBefore

source roles = [2, 5, [10, 33], [13, 36]]

After

derived = [[[10, 13, 0, 0], [10, 36, 23, 0], [33, 13, 43, 13], [33, 36, 20, 13]], [0, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S056





S058 · impliesBefore

source roles = [2, 6, [10, 33], [14, 37]]

After

derived = [[[10, 14, 1, 1], [10, 37, 24, 1], [33, 14, 42, 11], [33, 37, 19, 11]], [1, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S057





S059 · impliesBefore

source roles = [2, 7, [10, 33], [15, 38]]

After

derived = [[[10, 15, 2, 12], [10, 38, 25, 12], [33, 15, 41, 10], [33, 38, 18, 10]], [10, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S058





S060 · impliesBefore

source roles = [2, 8, [10, 33], [16, 39]]

After

derived = [[[10, 16, 3, 16], [10, 39, 26, 16], [33, 16, 40, 9], [33, 39, 17, 9]], [9, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S059





S061 · impliesBefore

source roles = [2, 9, [10, 33], [17, 40]]

After

derived = [[[10, 17, 4, 17], [10, 40, 27, 17], [33, 17, 39, 8], [33, 40, 16, 8]], [8, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S060





S062 · impliesBefore

source roles = [2, 10, [10, 33], [18, 41]]

After

derived = [[[10, 18, 5, 18], [10, 41, 28, 18], [33, 18, 38, 7], [33, 41, 15, 7]], [7, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S061





S063 · impliesBefore

source roles = [2, 11, [10, 33], [19, 42]]

After

derived = [[[10, 19, 6, 19], [10, 42, 29, 19], [33, 19, 37, 6], [33, 42, 14, 6]], [6, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S062





S064 · impliesBefore

source roles = [2, 12, [10, 33], [2, 25]]

After

derived = [[[10, 2, 12, 4], [10, 25, 35, 4], [33, 2, 31, 21], [33, 25, 8, 21]], [4, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S063





S065 · impliesBefore

source roles = [2, 13, [10, 33], [20, 43]]

After

derived = [[[10, 20, 7, 20], [10, 43, 30, 20], [33, 20, 36, 5], [33, 43, 13, 5]], [5, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S064





S066 · impliesBefore

source roles = [2, 14, [10, 33], [21, 44]]

After

derived = [[[10, 21, 8, 21], [10, 44, 31, 21], [33, 21, 35, 4], [33, 44, 12, 4]], [4, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S065





S067 · impliesBefore

source roles = [2, 15, [10, 33], [22, 45]]

After

derived = [[[10, 22, 9, 22], [10, 45, 32, 22], [33, 22, 34, 3], [33, 45, 11, 3]], [3, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S066





S068 · impliesBefore

source roles = [2, 16, [10, 33], [3, 26]]

After

derived = [[[10, 3, 13, 5], [10, 26, 36, 5], [33, 3, 30, 20], [33, 26, 7, 20]], [5, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S067





S069 · impliesBefore

source roles = [2, 17, [10, 33], [4, 27]]

After

derived = [[[10, 4, 14, 6], [10, 27, 37, 6], [33, 4, 29, 19], [33, 27, 6, 19]], [6, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S068





S070 · impliesBefore

source roles = [2, 18, [10, 33], [5, 28]]

After

derived = [[[10, 5, 15, 7], [10, 28, 38, 7], [33, 5, 28, 18], [33, 28, 5, 18]], [7, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S069





S071 · impliesBefore

source roles = [2, 19, [10, 33], [6, 29]]

After

derived = [[[10, 6, 16, 8], [10, 29, 39, 8], [33, 6, 27, 17], [33, 29, 4, 17]], [8, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S070





S072 · impliesBefore

source roles = [2, 20, [10, 33], [7, 30]]

After

derived = [[[10, 7, 17, 9], [10, 30, 40, 9], [33, 7, 26, 16], [33, 30, 3, 16]], [9, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S071





S073 · impliesBefore

source roles = [2, 21, [10, 33], [8, 31]]

After

derived = [[[10, 8, 18, 10], [10, 31, 41, 10], [33, 8, 25, 12], [33, 31, 2, 12]], [10, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S072





S074 · impliesBefore

source roles = [2, 22, [10, 33], [9, 32]]

After

derived = [[[10, 9, 19, 11], [10, 32, 42, 11], [33, 9, 24, 1], [33, 32, 1, 1]], [1, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S073





S075 · impliesBefore

source roles = [3, 0, [11, 34], [0, 23]]

After

derived = [[[11, 0, 11, 3], [11, 23, 34, 3], [34, 0, 34, 3], [34, 23, 11, 3]], [3], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S074





S076 · impliesBefore

source roles = [3, 1, [11, 34], [1, 24]]

After

derived = [[[11, 1, 12, 4], [11, 24, 35, 4], [34, 1, 33, 2], [34, 24, 10, 2]], [2, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S075





S077 · impliesBefore

source roles = [3, 2, [11, 34], [10, 33]]

After

derived = [[[11, 10, 21, 14], [11, 33, 44, 14], [34, 10, 24, 1], [34, 33, 1, 1]], [1, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S076





S078 · impliesBefore

source roles = [3, 3, [11, 34], [11, 34]]

After

derived = [[[11, 11, 22, 15], [11, 34, 45, 15], [34, 11, 23, 0], [34, 34, 0, 0]], [0, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S077





S079 · impliesBefore

source roles = [3, 4, [11, 34], [12, 35]]

After

derived = [[[11, 12, 0, 0], [11, 35, 23, 0], [34, 12, 45, 15], [34, 35, 22, 15]], [0, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S078





S080 · impliesBefore

source roles = [3, 5, [11, 34], [13, 36]]

After

derived = [[[11, 13, 1, 1], [11, 36, 24, 1], [34, 13, 44, 14], [34, 36, 21, 14]], [1, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S079





S081 · impliesBefore

source roles = [3, 6, [11, 34], [14, 37]]

After

derived = [[[11, 14, 2, 12], [11, 37, 25, 12], [34, 14, 43, 13], [34, 37, 20, 13]], [12, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S080





S082 · impliesBefore

source roles = [3, 7, [11, 34], [15, 38]]

After

derived = [[[11, 15, 3, 16], [11, 38, 26, 16], [34, 15, 42, 11], [34, 38, 19, 11]], [11, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S081





S083 · impliesBefore

source roles = [3, 8, [11, 34], [16, 39]]

After

derived = [[[11, 16, 4, 17], [11, 39, 27, 17], [34, 16, 41, 10], [34, 39, 18, 10]], [10, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S082





S084 · impliesBefore

source roles = [3, 9, [11, 34], [17, 40]]

After

derived = [[[11, 17, 5, 18], [11, 40, 28, 18], [34, 17, 40, 9], [34, 40, 17, 9]], [9, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S083





S085 · impliesBefore

source roles = [3, 10, [11, 34], [18, 41]]

After

derived = [[[11, 18, 6, 19], [11, 41, 29, 19], [34, 18, 39, 8], [34, 41, 16, 8]], [8, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S084





S086 · impliesBefore

source roles = [3, 11, [11, 34], [19, 42]]

After

derived = [[[11, 19, 7, 20], [11, 42, 30, 20], [34, 19, 38, 7], [34, 42, 15, 7]], [7, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S085





S087 · impliesBefore

source roles = [3, 12, [11, 34], [2, 25]]

After

derived = [[[11, 2, 13, 5], [11, 25, 36, 5], [34, 2, 32, 22], [34, 25, 9, 22]], [5, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S086





S088 · impliesBefore

source roles = [3, 13, [11, 34], [20, 43]]

After

derived = [[[11, 20, 8, 21], [11, 43, 31, 21], [34, 20, 37, 6], [34, 43, 14, 6]], [6, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S087





S089 · impliesBefore

source roles = [3, 14, [11, 34], [21, 44]]

After

derived = [[[11, 21, 9, 22], [11, 44, 32, 22], [34, 21, 36, 5], [34, 44, 13, 5]], [5, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S088





S090 · impliesBefore

source roles = [3, 15, [11, 34], [22, 45]]

After

derived = [[[11, 22, 10, 2], [11, 45, 33, 2], [34, 22, 35, 4], [34, 45, 12, 4]], [2, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S089





S091 · impliesBefore

source roles = [3, 16, [11, 34], [3, 26]]

After

derived = [[[11, 3, 14, 6], [11, 26, 37, 6], [34, 3, 31, 21], [34, 26, 8, 21]], [6, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S090





S092 · impliesBefore

source roles = [3, 17, [11, 34], [4, 27]]

After

derived = [[[11, 4, 15, 7], [11, 27, 38, 7], [34, 4, 30, 20], [34, 27, 7, 20]], [7, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S091





S093 · impliesBefore

source roles = [3, 18, [11, 34], [5, 28]]

After

derived = [[[11, 5, 16, 8], [11, 28, 39, 8], [34, 5, 29, 19], [34, 28, 6, 19]], [8, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S092





S094 · impliesBefore

source roles = [3, 19, [11, 34], [6, 29]]

After

derived = [[[11, 6, 17, 9], [11, 29, 40, 9], [34, 6, 28, 18], [34, 29, 5, 18]], [9, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S093





S095 · impliesBefore

source roles = [3, 20, [11, 34], [7, 30]]

After

derived = [[[11, 7, 18, 10], [11, 30, 41, 10], [34, 7, 27, 17], [34, 30, 4, 17]], [10, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S094





S096 · impliesBefore

source roles = [3, 21, [11, 34], [8, 31]]

After

derived = [[[11, 8, 19, 11], [11, 31, 42, 11], [34, 8, 26, 16], [34, 31, 3, 16]], [11, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S095





S097 · impliesBefore

source roles = [3, 22, [11, 34], [9, 32]]

After

derived = [[[11, 9, 20, 13], [11, 32, 43, 13], [34, 9, 25, 12], [34, 32, 2, 12]], [12, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S096





S098 · impliesBefore

source roles = [4, 0, [12, 35], [0, 23]]

After

derived = [[[12, 0, 12, 4], [12, 23, 35, 4], [35, 0, 35, 4], [35, 23, 12, 4]], [4], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S097





S099 · impliesBefore

source roles = [4, 1, [12, 35], [1, 24]]

After

derived = [[[12, 1, 13, 5], [12, 24, 36, 5], [35, 1, 34, 3], [35, 24, 11, 3]], [3, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S098





S100 · impliesBefore

source roles = [4, 2, [12, 35], [10, 33]]

After

derived = [[[12, 10, 22, 15], [12, 33, 45, 15], [35, 10, 25, 12], [35, 33, 2, 12]], [12, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S099





S101 · impliesBefore

source roles = [4, 3, [12, 35], [11, 34]]

After

derived = [[[12, 11, 0, 0], [12, 34, 23, 0], [35, 11, 24, 1], [35, 34, 1, 1]], [0, 1], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S100





S102 · impliesBefore

source roles = [4, 4, [12, 35], [12, 35]]

After

derived = [[[12, 12, 1, 1], [12, 35, 24, 1], [35, 12, 23, 0], [35, 35, 0, 0]], [0, 1], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S101





S103 · impliesBefore

source roles = [4, 5, [12, 35], [13, 36]]

After

derived = [[[12, 13, 2, 12], [12, 36, 25, 12], [35, 13, 45, 15], [35, 36, 22, 15]], [12, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S102





S104 · impliesBefore

source roles = [4, 6, [12, 35], [14, 37]]

After

derived = [[[12, 14, 3, 16], [12, 37, 26, 16], [35, 14, 44, 14], [35, 37, 21, 14]], [14, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S103





S105 · impliesBefore

source roles = [4, 7, [12, 35], [15, 38]]

After

derived = [[[12, 15, 4, 17], [12, 38, 27, 17], [35, 15, 43, 13], [35, 38, 20, 13]], [13, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S104





S106 · impliesBefore

source roles = [4, 8, [12, 35], [16, 39]]

After

derived = [[[12, 16, 5, 18], [12, 39, 28, 18], [35, 16, 42, 11], [35, 39, 19, 11]], [11, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S105





S107 · impliesBefore

source roles = [4, 9, [12, 35], [17, 40]]

After

derived = [[[12, 17, 6, 19], [12, 40, 29, 19], [35, 17, 41, 10], [35, 40, 18, 10]], [10, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S106





S108 · impliesBefore

source roles = [4, 10, [12, 35], [18, 41]]

After

derived = [[[12, 18, 7, 20], [12, 41, 30, 20], [35, 18, 40, 9], [35, 41, 17, 9]], [9, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S107





S109 · impliesBefore

source roles = [4, 11, [12, 35], [19, 42]]

After

derived = [[[12, 19, 8, 21], [12, 42, 31, 21], [35, 19, 39, 8], [35, 42, 16, 8]], [8, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S108





S110 · impliesBefore

source roles = [4, 12, [12, 35], [2, 25]]

After

derived = [[[12, 2, 14, 6], [12, 25, 37, 6], [35, 2, 33, 2], [35, 25, 10, 2]], [2, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S109





S111 · impliesBefore

source roles = [4, 13, [12, 35], [20, 43]]

After

derived = [[[12, 20, 9, 22], [12, 43, 32, 22], [35, 20, 38, 7], [35, 43, 15, 7]], [7, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S110





S112 · impliesBefore

source roles = [4, 14, [12, 35], [21, 44]]

After

derived = [[[12, 21, 10, 2], [12, 44, 33, 2], [35, 21, 37, 6], [35, 44, 14, 6]], [2, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S111





S113 · impliesBefore

source roles = [4, 15, [12, 35], [22, 45]]

After

derived = [[[12, 22, 11, 3], [12, 45, 34, 3], [35, 22, 36, 5], [35, 45, 13, 5]], [3, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S112





S114 · impliesBefore

source roles = [4, 16, [12, 35], [3, 26]]

After

derived = [[[12, 3, 15, 7], [12, 26, 38, 7], [35, 3, 32, 22], [35, 26, 9, 22]], [7, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S113





S115 · impliesBefore

source roles = [4, 17, [12, 35], [4, 27]]

After

derived = [[[12, 4, 16, 8], [12, 27, 39, 8], [35, 4, 31, 21], [35, 27, 8, 21]], [8, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S114





S116 · impliesBefore

source roles = [4, 18, [12, 35], [5, 28]]

After

derived = [[[12, 5, 17, 9], [12, 28, 40, 9], [35, 5, 30, 20], [35, 28, 7, 20]], [9, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S115





S117 · impliesBefore

source roles = [4, 19, [12, 35], [6, 29]]

After

derived = [[[12, 6, 18, 10], [12, 29, 41, 10], [35, 6, 29, 19], [35, 29, 6, 19]], [10, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S116





S118 · impliesBefore

source roles = [4, 20, [12, 35], [7, 30]]

After

derived = [[[12, 7, 19, 11], [12, 30, 42, 11], [35, 7, 28, 18], [35, 30, 5, 18]], [11, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S117





S119 · impliesBefore

source roles = [4, 21, [12, 35], [8, 31]]

After

derived = [[[12, 8, 20, 13], [12, 31, 43, 13], [35, 8, 27, 17], [35, 31, 4, 17]], [13, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S118





S120 · impliesBefore

source roles = [4, 22, [12, 35], [9, 32]]

After

derived = [[[12, 9, 21, 14], [12, 32, 44, 14], [35, 9, 26, 16], [35, 32, 3, 16]], [14, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S119





S121 · impliesBefore

source roles = [5, 0, [13, 36], [0, 23]]

After

derived = [[[13, 0, 13, 5], [13, 23, 36, 5], [36, 0, 36, 5], [36, 23, 13, 5]], [5], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S120





S122 · impliesBefore

source roles = [5, 1, [13, 36], [1, 24]]

After

derived = [[[13, 1, 14, 6], [13, 24, 37, 6], [36, 1, 35, 4], [36, 24, 12, 4]], [4, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S121





S123 · impliesBefore

source roles = [5, 2, [13, 36], [10, 33]]

After

derived = [[[13, 10, 0, 0], [13, 33, 23, 0], [36, 10, 26, 16], [36, 33, 3, 16]], [0, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S122





S124 · impliesBefore

source roles = [5, 3, [13, 36], [11, 34]]

After

derived = [[[13, 11, 1, 1], [13, 34, 24, 1], [36, 11, 25, 12], [36, 34, 2, 12]], [1, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S123





S125 · impliesBefore

source roles = [5, 4, [13, 36], [12, 35]]

After

derived = [[[13, 12, 2, 12], [13, 35, 25, 12], [36, 12, 24, 1], [36, 35, 1, 1]], [1, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S124





S126 · impliesBefore

source roles = [5, 5, [13, 36], [13, 36]]

After

derived = [[[13, 13, 3, 16], [13, 36, 26, 16], [36, 13, 23, 0], [36, 36, 0, 0]], [0, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S125





S127 · impliesBefore

source roles = [5, 6, [13, 36], [14, 37]]

After

derived = [[[13, 14, 4, 17], [13, 37, 27, 17], [36, 14, 45, 15], [36, 37, 22, 15]], [15, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S126





S128 · impliesBefore

source roles = [5, 7, [13, 36], [15, 38]]

After

derived = [[[13, 15, 5, 18], [13, 38, 28, 18], [36, 15, 44, 14], [36, 38, 21, 14]], [14, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S127





S129 · impliesBefore

source roles = [5, 8, [13, 36], [16, 39]]

After

derived = [[[13, 16, 6, 19], [13, 39, 29, 19], [36, 16, 43, 13], [36, 39, 20, 13]], [13, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S128





S130 · impliesBefore

source roles = [5, 9, [13, 36], [17, 40]]

After

derived = [[[13, 17, 7, 20], [13, 40, 30, 20], [36, 17, 42, 11], [36, 40, 19, 11]], [11, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S129





S131 · impliesBefore

source roles = [5, 10, [13, 36], [18, 41]]

After

derived = [[[13, 18, 8, 21], [13, 41, 31, 21], [36, 18, 41, 10], [36, 41, 18, 10]], [10, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S130





S132 · impliesBefore

source roles = [5, 11, [13, 36], [19, 42]]

After

derived = [[[13, 19, 9, 22], [13, 42, 32, 22], [36, 19, 40, 9], [36, 42, 17, 9]], [9, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S131





S133 · impliesBefore

source roles = [5, 12, [13, 36], [2, 25]]

After

derived = [[[13, 2, 15, 7], [13, 25, 38, 7], [36, 2, 34, 3], [36, 25, 11, 3]], [3, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S132





S134 · impliesBefore

source roles = [5, 13, [13, 36], [20, 43]]

After

derived = [[[13, 20, 10, 2], [13, 43, 33, 2], [36, 20, 39, 8], [36, 43, 16, 8]], [2, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S133





S135 · impliesBefore

source roles = [5, 14, [13, 36], [21, 44]]

After

derived = [[[13, 21, 11, 3], [13, 44, 34, 3], [36, 21, 38, 7], [36, 44, 15, 7]], [3, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S134





S136 · impliesBefore

source roles = [5, 15, [13, 36], [22, 45]]

After

derived = [[[13, 22, 12, 4], [13, 45, 35, 4], [36, 22, 37, 6], [36, 45, 14, 6]], [4, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S135





S137 · impliesBefore

source roles = [5, 16, [13, 36], [3, 26]]

After

derived = [[[13, 3, 16, 8], [13, 26, 39, 8], [36, 3, 33, 2], [36, 26, 10, 2]], [2, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S136





S138 · impliesBefore

source roles = [5, 17, [13, 36], [4, 27]]

After

derived = [[[13, 4, 17, 9], [13, 27, 40, 9], [36, 4, 32, 22], [36, 27, 9, 22]], [9, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S137





S139 · impliesBefore

source roles = [5, 18, [13, 36], [5, 28]]

After

derived = [[[13, 5, 18, 10], [13, 28, 41, 10], [36, 5, 31, 21], [36, 28, 8, 21]], [10, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S138





S140 · impliesBefore

source roles = [5, 19, [13, 36], [6, 29]]

After

derived = [[[13, 6, 19, 11], [13, 29, 42, 11], [36, 6, 30, 20], [36, 29, 7, 20]], [11, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S139





S141 · impliesBefore

source roles = [5, 20, [13, 36], [7, 30]]

After

derived = [[[13, 7, 20, 13], [13, 30, 43, 13], [36, 7, 29, 19], [36, 30, 6, 19]], [13, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S140





S142 · impliesBefore

source roles = [5, 21, [13, 36], [8, 31]]

After

derived = [[[13, 8, 21, 14], [13, 31, 44, 14], [36, 8, 28, 18], [36, 31, 5, 18]], [14, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S141





S143 · impliesBefore

source roles = [5, 22, [13, 36], [9, 32]]

After

derived = [[[13, 9, 22, 15], [13, 32, 45, 15], [36, 9, 27, 17], [36, 32, 4, 17]], [15, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S142





S144 · impliesBefore

source roles = [6, 0, [14, 37], [0, 23]]

After

derived = [[[14, 0, 14, 6], [14, 23, 37, 6], [37, 0, 37, 6], [37, 23, 14, 6]], [6], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S143





S145 · impliesBefore

source roles = [6, 1, [14, 37], [1, 24]]

After

derived = [[[14, 1, 15, 7], [14, 24, 38, 7], [37, 1, 36, 5], [37, 24, 13, 5]], [5, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S144





S146 · impliesBefore

source roles = [6, 2, [14, 37], [10, 33]]

After

derived = [[[14, 10, 1, 1], [14, 33, 24, 1], [37, 10, 27, 17], [37, 33, 4, 17]], [1, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S145





S147 · impliesBefore

source roles = [6, 3, [14, 37], [11, 34]]

After

derived = [[[14, 11, 2, 12], [14, 34, 25, 12], [37, 11, 26, 16], [37, 34, 3, 16]], [12, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S146





S148 · impliesBefore

source roles = [6, 4, [14, 37], [12, 35]]

After

derived = [[[14, 12, 3, 16], [14, 35, 26, 16], [37, 12, 25, 12], [37, 35, 2, 12]], [12, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S147





S149 · impliesBefore

source roles = [6, 5, [14, 37], [13, 36]]

After

derived = [[[14, 13, 4, 17], [14, 36, 27, 17], [37, 13, 24, 1], [37, 36, 1, 1]], [1, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S148





S150 · impliesBefore

source roles = [6, 6, [14, 37], [14, 37]]

After

derived = [[[14, 14, 5, 18], [14, 37, 28, 18], [37, 14, 23, 0], [37, 37, 0, 0]], [0, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S149





S151 · impliesBefore

source roles = [6, 7, [14, 37], [15, 38]]

After

derived = [[[14, 15, 6, 19], [14, 38, 29, 19], [37, 15, 45, 15], [37, 38, 22, 15]], [15, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S150





S152 · impliesBefore

source roles = [6, 8, [14, 37], [16, 39]]

After

derived = [[[14, 16, 7, 20], [14, 39, 30, 20], [37, 16, 44, 14], [37, 39, 21, 14]], [14, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S151





S153 · impliesBefore

source roles = [6, 9, [14, 37], [17, 40]]

After

derived = [[[14, 17, 8, 21], [14, 40, 31, 21], [37, 17, 43, 13], [37, 40, 20, 13]], [13, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S152





S154 · impliesBefore

source roles = [6, 10, [14, 37], [18, 41]]

After

derived = [[[14, 18, 9, 22], [14, 41, 32, 22], [37, 18, 42, 11], [37, 41, 19, 11]], [11, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S153





S155 · impliesBefore

source roles = [6, 11, [14, 37], [19, 42]]

After

derived = [[[14, 19, 10, 2], [14, 42, 33, 2], [37, 19, 41, 10], [37, 42, 18, 10]], [2, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S154





S156 · impliesBefore

source roles = [6, 12, [14, 37], [2, 25]]

After

derived = [[[14, 2, 16, 8], [14, 25, 39, 8], [37, 2, 35, 4], [37, 25, 12, 4]], [4, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S155





S157 · impliesBefore

source roles = [6, 13, [14, 37], [20, 43]]

After

derived = [[[14, 20, 11, 3], [14, 43, 34, 3], [37, 20, 40, 9], [37, 43, 17, 9]], [3, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S156





S158 · impliesBefore

source roles = [6, 14, [14, 37], [21, 44]]

After

derived = [[[14, 21, 12, 4], [14, 44, 35, 4], [37, 21, 39, 8], [37, 44, 16, 8]], [4, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S157





S159 · impliesBefore

source roles = [6, 15, [14, 37], [22, 45]]

After

derived = [[[14, 22, 13, 5], [14, 45, 36, 5], [37, 22, 38, 7], [37, 45, 15, 7]], [5, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S158





S160 · impliesBefore

source roles = [6, 16, [14, 37], [3, 26]]

After

derived = [[[14, 3, 17, 9], [14, 26, 40, 9], [37, 3, 34, 3], [37, 26, 11, 3]], [3, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S159





S161 · impliesBefore

source roles = [6, 17, [14, 37], [4, 27]]

After

derived = [[[14, 4, 18, 10], [14, 27, 41, 10], [37, 4, 33, 2], [37, 27, 10, 2]], [2, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S160





S162 · impliesBefore

source roles = [6, 18, [14, 37], [5, 28]]

After

derived = [[[14, 5, 19, 11], [14, 28, 42, 11], [37, 5, 32, 22], [37, 28, 9, 22]], [11, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S161





S163 · impliesBefore

source roles = [6, 19, [14, 37], [6, 29]]

After

derived = [[[14, 6, 20, 13], [14, 29, 43, 13], [37, 6, 31, 21], [37, 29, 8, 21]], [13, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S162





S164 · impliesBefore

source roles = [6, 20, [14, 37], [7, 30]]

After

derived = [[[14, 7, 21, 14], [14, 30, 44, 14], [37, 7, 30, 20], [37, 30, 7, 20]], [14, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S163





S165 · impliesBefore

source roles = [6, 21, [14, 37], [8, 31]]

After

derived = [[[14, 8, 22, 15], [14, 31, 45, 15], [37, 8, 29, 19], [37, 31, 6, 19]], [15, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S164





S166 · impliesBefore

source roles = [6, 22, [14, 37], [9, 32]]

After

derived = [[[14, 9, 0, 0], [14, 32, 23, 0], [37, 9, 28, 18], [37, 32, 5, 18]], [0, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S165





S167 · impliesBefore

source roles = [7, 0, [15, 38], [0, 23]]

After

derived = [[[15, 0, 15, 7], [15, 23, 38, 7], [38, 0, 38, 7], [38, 23, 15, 7]], [7], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S166





S168 · impliesBefore

source roles = [7, 1, [15, 38], [1, 24]]

After

derived = [[[15, 1, 16, 8], [15, 24, 39, 8], [38, 1, 37, 6], [38, 24, 14, 6]], [6, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S167





S169 · impliesBefore

source roles = [7, 2, [15, 38], [10, 33]]

After

derived = [[[15, 10, 2, 12], [15, 33, 25, 12], [38, 10, 28, 18], [38, 33, 5, 18]], [12, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S168





S170 · impliesBefore

source roles = [7, 3, [15, 38], [11, 34]]

After

derived = [[[15, 11, 3, 16], [15, 34, 26, 16], [38, 11, 27, 17], [38, 34, 4, 17]], [16, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S169





S171 · impliesBefore

source roles = [7, 4, [15, 38], [12, 35]]

After

derived = [[[15, 12, 4, 17], [15, 35, 27, 17], [38, 12, 26, 16], [38, 35, 3, 16]], [16, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S170





S172 · impliesBefore

source roles = [7, 5, [15, 38], [13, 36]]

After

derived = [[[15, 13, 5, 18], [15, 36, 28, 18], [38, 13, 25, 12], [38, 36, 2, 12]], [12, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S171





S173 · impliesBefore

source roles = [7, 6, [15, 38], [14, 37]]

After

derived = [[[15, 14, 6, 19], [15, 37, 29, 19], [38, 14, 24, 1], [38, 37, 1, 1]], [1, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S172





S174 · impliesBefore

source roles = [7, 7, [15, 38], [15, 38]]

After

derived = [[[15, 15, 7, 20], [15, 38, 30, 20], [38, 15, 23, 0], [38, 38, 0, 0]], [0, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S173





S175 · impliesBefore

source roles = [7, 8, [15, 38], [16, 39]]

After

derived = [[[15, 16, 8, 21], [15, 39, 31, 21], [38, 16, 45, 15], [38, 39, 22, 15]], [15, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S174





S176 · impliesBefore

source roles = [7, 9, [15, 38], [17, 40]]

After

derived = [[[15, 17, 9, 22], [15, 40, 32, 22], [38, 17, 44, 14], [38, 40, 21, 14]], [14, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S175





S177 · impliesBefore

source roles = [7, 10, [15, 38], [18, 41]]

After

derived = [[[15, 18, 10, 2], [15, 41, 33, 2], [38, 18, 43, 13], [38, 41, 20, 13]], [2, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S176





S178 · impliesBefore

source roles = [7, 11, [15, 38], [19, 42]]

After

derived = [[[15, 19, 11, 3], [15, 42, 34, 3], [38, 19, 42, 11], [38, 42, 19, 11]], [3, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S177





S179 · impliesBefore

source roles = [7, 12, [15, 38], [2, 25]]

After

derived = [[[15, 2, 17, 9], [15, 25, 40, 9], [38, 2, 36, 5], [38, 25, 13, 5]], [5, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S178





S180 · impliesBefore

source roles = [7, 13, [15, 38], [20, 43]]

After

derived = [[[15, 20, 12, 4], [15, 43, 35, 4], [38, 20, 41, 10], [38, 43, 18, 10]], [4, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S179





S181 · impliesBefore

source roles = [7, 14, [15, 38], [21, 44]]

After

derived = [[[15, 21, 13, 5], [15, 44, 36, 5], [38, 21, 40, 9], [38, 44, 17, 9]], [5, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S180





S182 · impliesBefore

source roles = [7, 15, [15, 38], [22, 45]]

After

derived = [[[15, 22, 14, 6], [15, 45, 37, 6], [38, 22, 39, 8], [38, 45, 16, 8]], [6, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S181





S183 · impliesBefore

source roles = [7, 16, [15, 38], [3, 26]]

After

derived = [[[15, 3, 18, 10], [15, 26, 41, 10], [38, 3, 35, 4], [38, 26, 12, 4]], [4, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S182





S184 · impliesBefore

source roles = [7, 17, [15, 38], [4, 27]]

After

derived = [[[15, 4, 19, 11], [15, 27, 42, 11], [38, 4, 34, 3], [38, 27, 11, 3]], [3, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S183





S185 · impliesBefore

source roles = [7, 18, [15, 38], [5, 28]]

After

derived = [[[15, 5, 20, 13], [15, 28, 43, 13], [38, 5, 33, 2], [38, 28, 10, 2]], [2, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S184





S186 · impliesBefore

source roles = [7, 19, [15, 38], [6, 29]]

After

derived = [[[15, 6, 21, 14], [15, 29, 44, 14], [38, 6, 32, 22], [38, 29, 9, 22]], [14, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S185





S187 · impliesBefore

source roles = [7, 20, [15, 38], [7, 30]]

After

derived = [[[15, 7, 22, 15], [15, 30, 45, 15], [38, 7, 31, 21], [38, 30, 8, 21]], [15, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S186





S188 · impliesBefore

source roles = [7, 21, [15, 38], [8, 31]]

After

derived = [[[15, 8, 0, 0], [15, 31, 23, 0], [38, 8, 30, 20], [38, 31, 7, 20]], [0, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S187





S189 · impliesBefore

source roles = [7, 22, [15, 38], [9, 32]]

After

derived = [[[15, 9, 1, 1], [15, 32, 24, 1], [38, 9, 29, 19], [38, 32, 6, 19]], [1, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S188





S190 · impliesBefore

source roles = [8, 0, [16, 39], [0, 23]]

After

derived = [[[16, 0, 16, 8], [16, 23, 39, 8], [39, 0, 39, 8], [39, 23, 16, 8]], [8], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S189





S191 · impliesBefore

source roles = [8, 1, [16, 39], [1, 24]]

After

derived = [[[16, 1, 17, 9], [16, 24, 40, 9], [39, 1, 38, 7], [39, 24, 15, 7]], [7, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S190





S192 · impliesBefore

source roles = [8, 2, [16, 39], [10, 33]]

After

derived = [[[16, 10, 3, 16], [16, 33, 26, 16], [39, 10, 29, 19], [39, 33, 6, 19]], [16, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S191





S193 · impliesBefore

source roles = [8, 3, [16, 39], [11, 34]]

After

derived = [[[16, 11, 4, 17], [16, 34, 27, 17], [39, 11, 28, 18], [39, 34, 5, 18]], [17, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S192





S194 · impliesBefore

source roles = [8, 4, [16, 39], [12, 35]]

After

derived = [[[16, 12, 5, 18], [16, 35, 28, 18], [39, 12, 27, 17], [39, 35, 4, 17]], [17, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S193





S195 · impliesBefore

source roles = [8, 5, [16, 39], [13, 36]]

After

derived = [[[16, 13, 6, 19], [16, 36, 29, 19], [39, 13, 26, 16], [39, 36, 3, 16]], [16, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S194





S196 · impliesBefore

source roles = [8, 6, [16, 39], [14, 37]]

After

derived = [[[16, 14, 7, 20], [16, 37, 30, 20], [39, 14, 25, 12], [39, 37, 2, 12]], [12, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S195





S197 · impliesBefore

source roles = [8, 7, [16, 39], [15, 38]]

After

derived = [[[16, 15, 8, 21], [16, 38, 31, 21], [39, 15, 24, 1], [39, 38, 1, 1]], [1, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S196





S198 · impliesBefore

source roles = [8, 8, [16, 39], [16, 39]]

After

derived = [[[16, 16, 9, 22], [16, 39, 32, 22], [39, 16, 23, 0], [39, 39, 0, 0]], [0, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S197





S199 · impliesBefore

source roles = [8, 9, [16, 39], [17, 40]]

After

derived = [[[16, 17, 10, 2], [16, 40, 33, 2], [39, 17, 45, 15], [39, 40, 22, 15]], [2, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S198





S200 · impliesBefore

source roles = [8, 10, [16, 39], [18, 41]]

After

derived = [[[16, 18, 11, 3], [16, 41, 34, 3], [39, 18, 44, 14], [39, 41, 21, 14]], [3, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S199





S201 · impliesBefore

source roles = [8, 11, [16, 39], [19, 42]]

After

derived = [[[16, 19, 12, 4], [16, 42, 35, 4], [39, 19, 43, 13], [39, 42, 20, 13]], [4, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S200





S202 · impliesBefore

source roles = [8, 12, [16, 39], [2, 25]]

After

derived = [[[16, 2, 18, 10], [16, 25, 41, 10], [39, 2, 37, 6], [39, 25, 14, 6]], [6, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S201





S203 · impliesBefore

source roles = [8, 13, [16, 39], [20, 43]]

After

derived = [[[16, 20, 13, 5], [16, 43, 36, 5], [39, 20, 42, 11], [39, 43, 19, 11]], [5, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S202





S204 · impliesBefore

source roles = [8, 14, [16, 39], [21, 44]]

After

derived = [[[16, 21, 14, 6], [16, 44, 37, 6], [39, 21, 41, 10], [39, 44, 18, 10]], [6, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S203





S205 · impliesBefore

source roles = [8, 15, [16, 39], [22, 45]]

After

derived = [[[16, 22, 15, 7], [16, 45, 38, 7], [39, 22, 40, 9], [39, 45, 17, 9]], [7, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S204





S206 · impliesBefore

source roles = [8, 16, [16, 39], [3, 26]]

After

derived = [[[16, 3, 19, 11], [16, 26, 42, 11], [39, 3, 36, 5], [39, 26, 13, 5]], [5, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S205





S207 · impliesBefore

source roles = [8, 17, [16, 39], [4, 27]]

After

derived = [[[16, 4, 20, 13], [16, 27, 43, 13], [39, 4, 35, 4], [39, 27, 12, 4]], [4, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S206





S208 · impliesBefore

source roles = [8, 18, [16, 39], [5, 28]]

After

derived = [[[16, 5, 21, 14], [16, 28, 44, 14], [39, 5, 34, 3], [39, 28, 11, 3]], [3, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S207





S209 · impliesBefore

source roles = [8, 19, [16, 39], [6, 29]]

After

derived = [[[16, 6, 22, 15], [16, 29, 45, 15], [39, 6, 33, 2], [39, 29, 10, 2]], [2, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S208





S210 · impliesBefore

source roles = [8, 20, [16, 39], [7, 30]]

After

derived = [[[16, 7, 0, 0], [16, 30, 23, 0], [39, 7, 32, 22], [39, 30, 9, 22]], [0, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S209





S211 · impliesBefore

source roles = [8, 21, [16, 39], [8, 31]]

After

derived = [[[16, 8, 1, 1], [16, 31, 24, 1], [39, 8, 31, 21], [39, 31, 8, 21]], [1, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S210





S212 · impliesBefore

source roles = [8, 22, [16, 39], [9, 32]]

After

derived = [[[16, 9, 2, 12], [16, 32, 25, 12], [39, 9, 30, 20], [39, 32, 7, 20]], [12, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S211





S213 · impliesBefore

source roles = [9, 0, [17, 40], [0, 23]]

After

derived = [[[17, 0, 17, 9], [17, 23, 40, 9], [40, 0, 40, 9], [40, 23, 17, 9]], [9], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S212





S214 · impliesBefore

source roles = [9, 1, [17, 40], [1, 24]]

After

derived = [[[17, 1, 18, 10], [17, 24, 41, 10], [40, 1, 39, 8], [40, 24, 16, 8]], [8, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S213





S215 · impliesBefore

source roles = [9, 2, [17, 40], [10, 33]]

After

derived = [[[17, 10, 4, 17], [17, 33, 27, 17], [40, 10, 30, 20], [40, 33, 7, 20]], [17, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S214





S216 · impliesBefore

source roles = [9, 3, [17, 40], [11, 34]]

After

derived = [[[17, 11, 5, 18], [17, 34, 28, 18], [40, 11, 29, 19], [40, 34, 6, 19]], [18, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S215





S217 · impliesBefore

source roles = [9, 4, [17, 40], [12, 35]]

After

derived = [[[17, 12, 6, 19], [17, 35, 29, 19], [40, 12, 28, 18], [40, 35, 5, 18]], [18, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S216





S218 · impliesBefore

source roles = [9, 5, [17, 40], [13, 36]]

After

derived = [[[17, 13, 7, 20], [17, 36, 30, 20], [40, 13, 27, 17], [40, 36, 4, 17]], [17, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S217





S219 · impliesBefore

source roles = [9, 6, [17, 40], [14, 37]]

After

derived = [[[17, 14, 8, 21], [17, 37, 31, 21], [40, 14, 26, 16], [40, 37, 3, 16]], [16, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S218





S220 · impliesBefore

source roles = [9, 7, [17, 40], [15, 38]]

After

derived = [[[17, 15, 9, 22], [17, 38, 32, 22], [40, 15, 25, 12], [40, 38, 2, 12]], [12, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S219





S221 · impliesBefore

source roles = [9, 8, [17, 40], [16, 39]]

After

derived = [[[17, 16, 10, 2], [17, 39, 33, 2], [40, 16, 24, 1], [40, 39, 1, 1]], [1, 2], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S220





S222 · impliesBefore

source roles = [9, 9, [17, 40], [17, 40]]

After

derived = [[[17, 17, 11, 3], [17, 40, 34, 3], [40, 17, 23, 0], [40, 40, 0, 0]], [0, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S221





S223 · impliesBefore

source roles = [9, 10, [17, 40], [18, 41]]

After

derived = [[[17, 18, 12, 4], [17, 41, 35, 4], [40, 18, 45, 15], [40, 41, 22, 15]], [4, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S222





S224 · impliesBefore

source roles = [9, 11, [17, 40], [19, 42]]

After

derived = [[[17, 19, 13, 5], [17, 42, 36, 5], [40, 19, 44, 14], [40, 42, 21, 14]], [5, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S223





S225 · impliesBefore

source roles = [9, 12, [17, 40], [2, 25]]

After

derived = [[[17, 2, 19, 11], [17, 25, 42, 11], [40, 2, 38, 7], [40, 25, 15, 7]], [7, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S224





S226 · impliesBefore

source roles = [9, 13, [17, 40], [20, 43]]

After

derived = [[[17, 20, 14, 6], [17, 43, 37, 6], [40, 20, 43, 13], [40, 43, 20, 13]], [6, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S225





S227 · impliesBefore

source roles = [9, 14, [17, 40], [21, 44]]

After

derived = [[[17, 21, 15, 7], [17, 44, 38, 7], [40, 21, 42, 11], [40, 44, 19, 11]], [7, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S226





S228 · impliesBefore

source roles = [9, 15, [17, 40], [22, 45]]

After

derived = [[[17, 22, 16, 8], [17, 45, 39, 8], [40, 22, 41, 10], [40, 45, 18, 10]], [8, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S227





S229 · impliesBefore

source roles = [9, 16, [17, 40], [3, 26]]

After

derived = [[[17, 3, 20, 13], [17, 26, 43, 13], [40, 3, 37, 6], [40, 26, 14, 6]], [6, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S228





S230 · impliesBefore

source roles = [9, 17, [17, 40], [4, 27]]

After

derived = [[[17, 4, 21, 14], [17, 27, 44, 14], [40, 4, 36, 5], [40, 27, 13, 5]], [5, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S229





S231 · impliesBefore

source roles = [9, 18, [17, 40], [5, 28]]

After

derived = [[[17, 5, 22, 15], [17, 28, 45, 15], [40, 5, 35, 4], [40, 28, 12, 4]], [4, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S230





S232 · impliesBefore

source roles = [9, 19, [17, 40], [6, 29]]

After

derived = [[[17, 6, 0, 0], [17, 29, 23, 0], [40, 6, 34, 3], [40, 29, 11, 3]], [0, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S231





S233 · impliesBefore

source roles = [9, 20, [17, 40], [7, 30]]

After

derived = [[[17, 7, 1, 1], [17, 30, 24, 1], [40, 7, 33, 2], [40, 30, 10, 2]], [1, 2], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S232





S234 · impliesBefore

source roles = [9, 21, [17, 40], [8, 31]]

After

derived = [[[17, 8, 2, 12], [17, 31, 25, 12], [40, 8, 32, 22], [40, 31, 9, 22]], [12, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S233





S235 · impliesBefore

source roles = [9, 22, [17, 40], [9, 32]]

After

derived = [[[17, 9, 3, 16], [17, 32, 26, 16], [40, 9, 31, 21], [40, 32, 8, 21]], [16, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S234





S236 · impliesBefore

source roles = [10, 0, [18, 41], [0, 23]]

After

derived = [[[18, 0, 18, 10], [18, 23, 41, 10], [41, 0, 41, 10], [41, 23, 18, 10]], [10], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S235





S237 · impliesBefore

source roles = [10, 1, [18, 41], [1, 24]]

After

derived = [[[18, 1, 19, 11], [18, 24, 42, 11], [41, 1, 40, 9], [41, 24, 17, 9]], [9, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S236





S238 · impliesBefore

source roles = [10, 2, [18, 41], [10, 33]]

After

derived = [[[18, 10, 5, 18], [18, 33, 28, 18], [41, 10, 31, 21], [41, 33, 8, 21]], [18, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S237





S239 · impliesBefore

source roles = [10, 3, [18, 41], [11, 34]]

After

derived = [[[18, 11, 6, 19], [18, 34, 29, 19], [41, 11, 30, 20], [41, 34, 7, 20]], [19, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S238





S240 · impliesBefore

source roles = [10, 4, [18, 41], [12, 35]]

After

derived = [[[18, 12, 7, 20], [18, 35, 30, 20], [41, 12, 29, 19], [41, 35, 6, 19]], [19, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S239





S241 · impliesBefore

source roles = [10, 5, [18, 41], [13, 36]]

After

derived = [[[18, 13, 8, 21], [18, 36, 31, 21], [41, 13, 28, 18], [41, 36, 5, 18]], [18, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S240





S242 · impliesBefore

source roles = [10, 6, [18, 41], [14, 37]]

After

derived = [[[18, 14, 9, 22], [18, 37, 32, 22], [41, 14, 27, 17], [41, 37, 4, 17]], [17, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S241





S243 · impliesBefore

source roles = [10, 7, [18, 41], [15, 38]]

After

derived = [[[18, 15, 10, 2], [18, 38, 33, 2], [41, 15, 26, 16], [41, 38, 3, 16]], [2, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S242





S244 · impliesBefore

source roles = [10, 8, [18, 41], [16, 39]]

After

derived = [[[18, 16, 11, 3], [18, 39, 34, 3], [41, 16, 25, 12], [41, 39, 2, 12]], [3, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S243





S245 · impliesBefore

source roles = [10, 9, [18, 41], [17, 40]]

After

derived = [[[18, 17, 12, 4], [18, 40, 35, 4], [41, 17, 24, 1], [41, 40, 1, 1]], [1, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S244





S246 · impliesBefore

source roles = [10, 10, [18, 41], [18, 41]]

After

derived = [[[18, 18, 13, 5], [18, 41, 36, 5], [41, 18, 23, 0], [41, 41, 0, 0]], [0, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S245





S247 · impliesBefore

source roles = [10, 11, [18, 41], [19, 42]]

After

derived = [[[18, 19, 14, 6], [18, 42, 37, 6], [41, 19, 45, 15], [41, 42, 22, 15]], [6, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S246





S248 · impliesBefore

source roles = [10, 12, [18, 41], [2, 25]]

After

derived = [[[18, 2, 20, 13], [18, 25, 43, 13], [41, 2, 39, 8], [41, 25, 16, 8]], [8, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S247





S249 · impliesBefore

source roles = [10, 13, [18, 41], [20, 43]]

After

derived = [[[18, 20, 15, 7], [18, 43, 38, 7], [41, 20, 44, 14], [41, 43, 21, 14]], [7, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S248





S250 · impliesBefore

source roles = [10, 14, [18, 41], [21, 44]]

After

derived = [[[18, 21, 16, 8], [18, 44, 39, 8], [41, 21, 43, 13], [41, 44, 20, 13]], [8, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S249





S251 · impliesBefore

source roles = [10, 15, [18, 41], [22, 45]]

After

derived = [[[18, 22, 17, 9], [18, 45, 40, 9], [41, 22, 42, 11], [41, 45, 19, 11]], [9, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S250





S252 · impliesBefore

source roles = [10, 16, [18, 41], [3, 26]]

After

derived = [[[18, 3, 21, 14], [18, 26, 44, 14], [41, 3, 38, 7], [41, 26, 15, 7]], [7, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S251





S253 · impliesBefore

source roles = [10, 17, [18, 41], [4, 27]]

After

derived = [[[18, 4, 22, 15], [18, 27, 45, 15], [41, 4, 37, 6], [41, 27, 14, 6]], [6, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S252





S254 · impliesBefore

source roles = [10, 18, [18, 41], [5, 28]]

After

derived = [[[18, 5, 0, 0], [18, 28, 23, 0], [41, 5, 36, 5], [41, 28, 13, 5]], [0, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S253





S255 · impliesBefore

source roles = [10, 19, [18, 41], [6, 29]]

After

derived = [[[18, 6, 1, 1], [18, 29, 24, 1], [41, 6, 35, 4], [41, 29, 12, 4]], [1, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S254





S256 · impliesBefore

source roles = [10, 20, [18, 41], [7, 30]]

After

derived = [[[18, 7, 2, 12], [18, 30, 25, 12], [41, 7, 34, 3], [41, 30, 11, 3]], [3, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S255





S257 · impliesBefore

source roles = [10, 21, [18, 41], [8, 31]]

After

derived = [[[18, 8, 3, 16], [18, 31, 26, 16], [41, 8, 33, 2], [41, 31, 10, 2]], [2, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S256





S258 · impliesBefore

source roles = [10, 22, [18, 41], [9, 32]]

After

derived = [[[18, 9, 4, 17], [18, 32, 27, 17], [41, 9, 32, 22], [41, 32, 9, 22]], [17, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S257





S259 · impliesBefore

source roles = [11, 0, [19, 42], [0, 23]]

After

derived = [[[19, 0, 19, 11], [19, 23, 42, 11], [42, 0, 42, 11], [42, 23, 19, 11]], [11], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S258





S260 · impliesBefore

source roles = [11, 1, [19, 42], [1, 24]]

After

derived = [[[19, 1, 20, 13], [19, 24, 43, 13], [42, 1, 41, 10], [42, 24, 18, 10]], [10, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S259





S261 · impliesBefore

source roles = [11, 2, [19, 42], [10, 33]]

After

derived = [[[19, 10, 6, 19], [19, 33, 29, 19], [42, 10, 32, 22], [42, 33, 9, 22]], [19, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S260





S262 · impliesBefore

source roles = [11, 3, [19, 42], [11, 34]]

After

derived = [[[19, 11, 7, 20], [19, 34, 30, 20], [42, 11, 31, 21], [42, 34, 8, 21]], [20, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S261





S263 · impliesBefore

source roles = [11, 4, [19, 42], [12, 35]]

After

derived = [[[19, 12, 8, 21], [19, 35, 31, 21], [42, 12, 30, 20], [42, 35, 7, 20]], [20, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S262





S264 · impliesBefore

source roles = [11, 5, [19, 42], [13, 36]]

After

derived = [[[19, 13, 9, 22], [19, 36, 32, 22], [42, 13, 29, 19], [42, 36, 6, 19]], [19, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S263





S265 · impliesBefore

source roles = [11, 6, [19, 42], [14, 37]]

After

derived = [[[19, 14, 10, 2], [19, 37, 33, 2], [42, 14, 28, 18], [42, 37, 5, 18]], [2, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S264





S266 · impliesBefore

source roles = [11, 7, [19, 42], [15, 38]]

After

derived = [[[19, 15, 11, 3], [19, 38, 34, 3], [42, 15, 27, 17], [42, 38, 4, 17]], [3, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S265





S267 · impliesBefore

source roles = [11, 8, [19, 42], [16, 39]]

After

derived = [[[19, 16, 12, 4], [19, 39, 35, 4], [42, 16, 26, 16], [42, 39, 3, 16]], [4, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S266





S268 · impliesBefore

source roles = [11, 9, [19, 42], [17, 40]]

After

derived = [[[19, 17, 13, 5], [19, 40, 36, 5], [42, 17, 25, 12], [42, 40, 2, 12]], [5, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S267





S269 · impliesBefore

source roles = [11, 10, [19, 42], [18, 41]]

After

derived = [[[19, 18, 14, 6], [19, 41, 37, 6], [42, 18, 24, 1], [42, 41, 1, 1]], [1, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S268





S270 · impliesBefore

source roles = [11, 11, [19, 42], [19, 42]]

After

derived = [[[19, 19, 15, 7], [19, 42, 38, 7], [42, 19, 23, 0], [42, 42, 0, 0]], [0, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S269





S271 · impliesBefore

source roles = [11, 12, [19, 42], [2, 25]]

After

derived = [[[19, 2, 21, 14], [19, 25, 44, 14], [42, 2, 40, 9], [42, 25, 17, 9]], [9, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S270





S272 · impliesBefore

source roles = [11, 13, [19, 42], [20, 43]]

After

derived = [[[19, 20, 16, 8], [19, 43, 39, 8], [42, 20, 45, 15], [42, 43, 22, 15]], [8, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S271





S273 · impliesBefore

source roles = [11, 14, [19, 42], [21, 44]]

After

derived = [[[19, 21, 17, 9], [19, 44, 40, 9], [42, 21, 44, 14], [42, 44, 21, 14]], [9, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S272





S274 · impliesBefore

source roles = [11, 15, [19, 42], [22, 45]]

After

derived = [[[19, 22, 18, 10], [19, 45, 41, 10], [42, 22, 43, 13], [42, 45, 20, 13]], [10, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S273





S275 · impliesBefore

source roles = [11, 16, [19, 42], [3, 26]]

After

derived = [[[19, 3, 22, 15], [19, 26, 45, 15], [42, 3, 39, 8], [42, 26, 16, 8]], [8, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S274





S276 · impliesBefore

source roles = [11, 17, [19, 42], [4, 27]]

After

derived = [[[19, 4, 0, 0], [19, 27, 23, 0], [42, 4, 38, 7], [42, 27, 15, 7]], [0, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S275





S277 · impliesBefore

source roles = [11, 18, [19, 42], [5, 28]]

After

derived = [[[19, 5, 1, 1], [19, 28, 24, 1], [42, 5, 37, 6], [42, 28, 14, 6]], [1, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S276





S278 · impliesBefore

source roles = [11, 19, [19, 42], [6, 29]]

After

derived = [[[19, 6, 2, 12], [19, 29, 25, 12], [42, 6, 36, 5], [42, 29, 13, 5]], [5, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S277





S279 · impliesBefore

source roles = [11, 20, [19, 42], [7, 30]]

After

derived = [[[19, 7, 3, 16], [19, 30, 26, 16], [42, 7, 35, 4], [42, 30, 12, 4]], [4, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S278





S280 · impliesBefore

source roles = [11, 21, [19, 42], [8, 31]]

After

derived = [[[19, 8, 4, 17], [19, 31, 27, 17], [42, 8, 34, 3], [42, 31, 11, 3]], [3, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S279





S281 · impliesBefore

source roles = [11, 22, [19, 42], [9, 32]]

After

derived = [[[19, 9, 5, 18], [19, 32, 28, 18], [42, 9, 33, 2], [42, 32, 10, 2]], [2, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S280





S282 · impliesBefore

source roles = [12, 0, [2, 25], [0, 23]]

After

derived = [[[2, 0, 2, 12], [2, 23, 25, 12], [25, 0, 25, 12], [25, 23, 2, 12]], [12], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S281





S283 · impliesBefore

source roles = [12, 1, [2, 25], [1, 24]]

After

derived = [[[2, 1, 3, 16], [2, 24, 26, 16], [25, 1, 24, 1], [25, 24, 1, 1]], [1, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S282





S284 · impliesBefore

source roles = [12, 2, [2, 25], [10, 33]]

After

derived = [[[2, 10, 12, 4], [2, 33, 35, 4], [25, 10, 38, 7], [25, 33, 15, 7]], [4, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S283





S285 · impliesBefore

source roles = [12, 3, [2, 25], [11, 34]]

After

derived = [[[2, 11, 13, 5], [2, 34, 36, 5], [25, 11, 37, 6], [25, 34, 14, 6]], [5, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S284





S286 · impliesBefore

source roles = [12, 4, [2, 25], [12, 35]]

After

derived = [[[2, 12, 14, 6], [2, 35, 37, 6], [25, 12, 36, 5], [25, 35, 13, 5]], [5, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S285





S287 · impliesBefore

source roles = [12, 5, [2, 25], [13, 36]]

After

derived = [[[2, 13, 15, 7], [2, 36, 38, 7], [25, 13, 35, 4], [25, 36, 12, 4]], [4, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S286





S288 · impliesBefore

source roles = [12, 6, [2, 25], [14, 37]]

After

derived = [[[2, 14, 16, 8], [2, 37, 39, 8], [25, 14, 34, 3], [25, 37, 11, 3]], [3, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S287





S289 · impliesBefore

source roles = [12, 7, [2, 25], [15, 38]]

After

derived = [[[2, 15, 17, 9], [2, 38, 40, 9], [25, 15, 33, 2], [25, 38, 10, 2]], [2, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S288





S290 · impliesBefore

source roles = [12, 8, [2, 25], [16, 39]]

After

derived = [[[2, 16, 18, 10], [2, 39, 41, 10], [25, 16, 32, 22], [25, 39, 9, 22]], [10, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S289





S291 · impliesBefore

source roles = [12, 9, [2, 25], [17, 40]]

After

derived = [[[2, 17, 19, 11], [2, 40, 42, 11], [25, 17, 31, 21], [25, 40, 8, 21]], [11, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S290





S292 · impliesBefore

source roles = [12, 10, [2, 25], [18, 41]]

After

derived = [[[2, 18, 20, 13], [2, 41, 43, 13], [25, 18, 30, 20], [25, 41, 7, 20]], [13, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S291





S293 · impliesBefore

source roles = [12, 11, [2, 25], [19, 42]]

After

derived = [[[2, 19, 21, 14], [2, 42, 44, 14], [25, 19, 29, 19], [25, 42, 6, 19]], [14, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S292





S294 · impliesBefore

source roles = [12, 12, [2, 25], [2, 25]]

After

derived = [[[2, 2, 4, 17], [2, 25, 27, 17], [25, 2, 23, 0], [25, 25, 0, 0]], [0, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S293





S295 · impliesBefore

source roles = [12, 13, [2, 25], [20, 43]]

After

derived = [[[2, 20, 22, 15], [2, 43, 45, 15], [25, 20, 28, 18], [25, 43, 5, 18]], [15, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S294





S296 · impliesBefore

source roles = [12, 14, [2, 25], [21, 44]]

After

derived = [[[2, 21, 0, 0], [2, 44, 23, 0], [25, 21, 27, 17], [25, 44, 4, 17]], [0, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S295





S297 · impliesBefore

source roles = [12, 15, [2, 25], [22, 45]]

After

derived = [[[2, 22, 1, 1], [2, 45, 24, 1], [25, 22, 26, 16], [25, 45, 3, 16]], [1, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S296





S298 · impliesBefore

source roles = [12, 16, [2, 25], [3, 26]]

After

derived = [[[2, 3, 5, 18], [2, 26, 28, 18], [25, 3, 45, 15], [25, 26, 22, 15]], [15, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S297





S299 · impliesBefore

source roles = [12, 17, [2, 25], [4, 27]]

After

derived = [[[2, 4, 6, 19], [2, 27, 29, 19], [25, 4, 44, 14], [25, 27, 21, 14]], [14, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S298





S300 · impliesBefore

source roles = [12, 18, [2, 25], [5, 28]]

After

derived = [[[2, 5, 7, 20], [2, 28, 30, 20], [25, 5, 43, 13], [25, 28, 20, 13]], [13, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S299





S301 · impliesBefore

source roles = [12, 19, [2, 25], [6, 29]]

After

derived = [[[2, 6, 8, 21], [2, 29, 31, 21], [25, 6, 42, 11], [25, 29, 19, 11]], [11, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S300





S302 · impliesBefore

source roles = [12, 20, [2, 25], [7, 30]]

After

derived = [[[2, 7, 9, 22], [2, 30, 32, 22], [25, 7, 41, 10], [25, 30, 18, 10]], [10, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S301





S303 · impliesBefore

source roles = [12, 21, [2, 25], [8, 31]]

After

derived = [[[2, 8, 10, 2], [2, 31, 33, 2], [25, 8, 40, 9], [25, 31, 17, 9]], [2, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S302





S304 · impliesBefore

source roles = [12, 22, [2, 25], [9, 32]]

After

derived = [[[2, 9, 11, 3], [2, 32, 34, 3], [25, 9, 39, 8], [25, 32, 16, 8]], [3, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S303





S305 · impliesBefore

source roles = [13, 0, [20, 43], [0, 23]]

After

derived = [[[20, 0, 20, 13], [20, 23, 43, 13], [43, 0, 43, 13], [43, 23, 20, 13]], [13], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S304





S306 · impliesBefore

source roles = [13, 1, [20, 43], [1, 24]]

After

derived = [[[20, 1, 21, 14], [20, 24, 44, 14], [43, 1, 42, 11], [43, 24, 19, 11]], [11, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S305





S307 · impliesBefore

source roles = [13, 2, [20, 43], [10, 33]]

After

derived = [[[20, 10, 7, 20], [20, 33, 30, 20], [43, 10, 33, 2], [43, 33, 10, 2]], [2, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S306





S308 · impliesBefore

source roles = [13, 3, [20, 43], [11, 34]]

After

derived = [[[20, 11, 8, 21], [20, 34, 31, 21], [43, 11, 32, 22], [43, 34, 9, 22]], [21, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S307





S309 · impliesBefore

source roles = [13, 4, [20, 43], [12, 35]]

After

derived = [[[20, 12, 9, 22], [20, 35, 32, 22], [43, 12, 31, 21], [43, 35, 8, 21]], [21, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S308





S310 · impliesBefore

source roles = [13, 5, [20, 43], [13, 36]]

After

derived = [[[20, 13, 10, 2], [20, 36, 33, 2], [43, 13, 30, 20], [43, 36, 7, 20]], [2, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S309





S311 · impliesBefore

source roles = [13, 6, [20, 43], [14, 37]]

After

derived = [[[20, 14, 11, 3], [20, 37, 34, 3], [43, 14, 29, 19], [43, 37, 6, 19]], [3, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S310





S312 · impliesBefore

source roles = [13, 7, [20, 43], [15, 38]]

After

derived = [[[20, 15, 12, 4], [20, 38, 35, 4], [43, 15, 28, 18], [43, 38, 5, 18]], [4, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S311





S313 · impliesBefore

source roles = [13, 8, [20, 43], [16, 39]]

After

derived = [[[20, 16, 13, 5], [20, 39, 36, 5], [43, 16, 27, 17], [43, 39, 4, 17]], [5, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S312





S314 · impliesBefore

source roles = [13, 9, [20, 43], [17, 40]]

After

derived = [[[20, 17, 14, 6], [20, 40, 37, 6], [43, 17, 26, 16], [43, 40, 3, 16]], [6, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S313





S315 · impliesBefore

source roles = [13, 10, [20, 43], [18, 41]]

After

derived = [[[20, 18, 15, 7], [20, 41, 38, 7], [43, 18, 25, 12], [43, 41, 2, 12]], [7, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S314





S316 · impliesBefore

source roles = [13, 11, [20, 43], [19, 42]]

After

derived = [[[20, 19, 16, 8], [20, 42, 39, 8], [43, 19, 24, 1], [43, 42, 1, 1]], [1, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S315





S317 · impliesBefore

source roles = [13, 12, [20, 43], [2, 25]]

After

derived = [[[20, 2, 22, 15], [20, 25, 45, 15], [43, 2, 41, 10], [43, 25, 18, 10]], [10, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S316





S318 · impliesBefore

source roles = [13, 13, [20, 43], [20, 43]]

After

derived = [[[20, 20, 17, 9], [20, 43, 40, 9], [43, 20, 23, 0], [43, 43, 0, 0]], [0, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S317





S319 · impliesBefore

source roles = [13, 14, [20, 43], [21, 44]]

After

derived = [[[20, 21, 18, 10], [20, 44, 41, 10], [43, 21, 45, 15], [43, 44, 22, 15]], [10, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S318





S320 · impliesBefore

source roles = [13, 15, [20, 43], [22, 45]]

After

derived = [[[20, 22, 19, 11], [20, 45, 42, 11], [43, 22, 44, 14], [43, 45, 21, 14]], [11, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S319





S321 · impliesBefore

source roles = [13, 16, [20, 43], [3, 26]]

After

derived = [[[20, 3, 0, 0], [20, 26, 23, 0], [43, 3, 40, 9], [43, 26, 17, 9]], [0, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S320





S322 · impliesBefore

source roles = [13, 17, [20, 43], [4, 27]]

After

derived = [[[20, 4, 1, 1], [20, 27, 24, 1], [43, 4, 39, 8], [43, 27, 16, 8]], [1, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S321





S323 · impliesBefore

source roles = [13, 18, [20, 43], [5, 28]]

After

derived = [[[20, 5, 2, 12], [20, 28, 25, 12], [43, 5, 38, 7], [43, 28, 15, 7]], [7, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S322





S324 · impliesBefore

source roles = [13, 19, [20, 43], [6, 29]]

After

derived = [[[20, 6, 3, 16], [20, 29, 26, 16], [43, 6, 37, 6], [43, 29, 14, 6]], [6, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S323





S325 · impliesBefore

source roles = [13, 20, [20, 43], [7, 30]]

After

derived = [[[20, 7, 4, 17], [20, 30, 27, 17], [43, 7, 36, 5], [43, 30, 13, 5]], [5, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S324





S326 · impliesBefore

source roles = [13, 21, [20, 43], [8, 31]]

After

derived = [[[20, 8, 5, 18], [20, 31, 28, 18], [43, 8, 35, 4], [43, 31, 12, 4]], [4, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S325





S327 · impliesBefore

source roles = [13, 22, [20, 43], [9, 32]]

After

derived = [[[20, 9, 6, 19], [20, 32, 29, 19], [43, 9, 34, 3], [43, 32, 11, 3]], [3, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S326





S328 · impliesBefore

source roles = [14, 0, [21, 44], [0, 23]]

After

derived = [[[21, 0, 21, 14], [21, 23, 44, 14], [44, 0, 44, 14], [44, 23, 21, 14]], [14], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S327





S329 · impliesBefore

source roles = [14, 1, [21, 44], [1, 24]]

After

derived = [[[21, 1, 22, 15], [21, 24, 45, 15], [44, 1, 43, 13], [44, 24, 20, 13]], [13, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S328





S330 · impliesBefore

source roles = [14, 2, [21, 44], [10, 33]]

After

derived = [[[21, 10, 8, 21], [21, 33, 31, 21], [44, 10, 34, 3], [44, 33, 11, 3]], [3, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S329





S331 · impliesBefore

source roles = [14, 3, [21, 44], [11, 34]]

After

derived = [[[21, 11, 9, 22], [21, 34, 32, 22], [44, 11, 33, 2], [44, 34, 10, 2]], [2, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S330





S332 · impliesBefore

source roles = [14, 4, [21, 44], [12, 35]]

After

derived = [[[21, 12, 10, 2], [21, 35, 33, 2], [44, 12, 32, 22], [44, 35, 9, 22]], [2, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S331





S333 · impliesBefore

source roles = [14, 5, [21, 44], [13, 36]]

After

derived = [[[21, 13, 11, 3], [21, 36, 34, 3], [44, 13, 31, 21], [44, 36, 8, 21]], [3, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S332





S334 · impliesBefore

source roles = [14, 6, [21, 44], [14, 37]]

After

derived = [[[21, 14, 12, 4], [21, 37, 35, 4], [44, 14, 30, 20], [44, 37, 7, 20]], [4, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S333





S335 · impliesBefore

source roles = [14, 7, [21, 44], [15, 38]]

After

derived = [[[21, 15, 13, 5], [21, 38, 36, 5], [44, 15, 29, 19], [44, 38, 6, 19]], [5, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S334





S336 · impliesBefore

source roles = [14, 8, [21, 44], [16, 39]]

After

derived = [[[21, 16, 14, 6], [21, 39, 37, 6], [44, 16, 28, 18], [44, 39, 5, 18]], [6, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S335





S337 · impliesBefore

source roles = [14, 9, [21, 44], [17, 40]]

After

derived = [[[21, 17, 15, 7], [21, 40, 38, 7], [44, 17, 27, 17], [44, 40, 4, 17]], [7, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S336





S338 · impliesBefore

source roles = [14, 10, [21, 44], [18, 41]]

After

derived = [[[21, 18, 16, 8], [21, 41, 39, 8], [44, 18, 26, 16], [44, 41, 3, 16]], [8, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S337





S339 · impliesBefore

source roles = [14, 11, [21, 44], [19, 42]]

After

derived = [[[21, 19, 17, 9], [21, 42, 40, 9], [44, 19, 25, 12], [44, 42, 2, 12]], [9, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S338





S340 · impliesBefore

source roles = [14, 12, [21, 44], [2, 25]]

After

derived = [[[21, 2, 0, 0], [21, 25, 23, 0], [44, 2, 42, 11], [44, 25, 19, 11]], [0, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S339





S341 · impliesBefore

source roles = [14, 13, [21, 44], [20, 43]]

After

derived = [[[21, 20, 18, 10], [21, 43, 41, 10], [44, 20, 24, 1], [44, 43, 1, 1]], [1, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S340





S342 · impliesBefore

source roles = [14, 14, [21, 44], [21, 44]]

After

derived = [[[21, 21, 19, 11], [21, 44, 42, 11], [44, 21, 23, 0], [44, 44, 0, 0]], [0, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S341





S343 · impliesBefore

source roles = [14, 15, [21, 44], [22, 45]]

After

derived = [[[21, 22, 20, 13], [21, 45, 43, 13], [44, 22, 45, 15], [44, 45, 22, 15]], [13, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S342





S344 · impliesBefore

source roles = [14, 16, [21, 44], [3, 26]]

After

derived = [[[21, 3, 1, 1], [21, 26, 24, 1], [44, 3, 41, 10], [44, 26, 18, 10]], [1, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S343





S345 · impliesBefore

source roles = [14, 17, [21, 44], [4, 27]]

After

derived = [[[21, 4, 2, 12], [21, 27, 25, 12], [44, 4, 40, 9], [44, 27, 17, 9]], [9, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S344





S346 · impliesBefore

source roles = [14, 18, [21, 44], [5, 28]]

After

derived = [[[21, 5, 3, 16], [21, 28, 26, 16], [44, 5, 39, 8], [44, 28, 16, 8]], [8, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S345





S347 · impliesBefore

source roles = [14, 19, [21, 44], [6, 29]]

After

derived = [[[21, 6, 4, 17], [21, 29, 27, 17], [44, 6, 38, 7], [44, 29, 15, 7]], [7, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S346





S348 · impliesBefore

source roles = [14, 20, [21, 44], [7, 30]]

After

derived = [[[21, 7, 5, 18], [21, 30, 28, 18], [44, 7, 37, 6], [44, 30, 14, 6]], [6, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S347





S349 · impliesBefore

source roles = [14, 21, [21, 44], [8, 31]]

After

derived = [[[21, 8, 6, 19], [21, 31, 29, 19], [44, 8, 36, 5], [44, 31, 13, 5]], [5, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S348





S350 · impliesBefore

source roles = [14, 22, [21, 44], [9, 32]]

After

derived = [[[21, 9, 7, 20], [21, 32, 30, 20], [44, 9, 35, 4], [44, 32, 12, 4]], [4, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S349





S351 · impliesBefore

source roles = [15, 0, [22, 45], [0, 23]]

After

derived = [[[22, 0, 22, 15], [22, 23, 45, 15], [45, 0, 45, 15], [45, 23, 22, 15]], [15], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S350





S352 · impliesBefore

source roles = [15, 1, [22, 45], [1, 24]]

After

derived = [[[22, 1, 0, 0], [22, 24, 23, 0], [45, 1, 44, 14], [45, 24, 21, 14]], [0, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S351





S353 · impliesBefore

source roles = [15, 2, [22, 45], [10, 33]]

After

derived = [[[22, 10, 9, 22], [22, 33, 32, 22], [45, 10, 35, 4], [45, 33, 12, 4]], [4, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S352





S354 · impliesBefore

source roles = [15, 3, [22, 45], [11, 34]]

After

derived = [[[22, 11, 10, 2], [22, 34, 33, 2], [45, 11, 34, 3], [45, 34, 11, 3]], [2, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S353





S355 · impliesBefore

source roles = [15, 4, [22, 45], [12, 35]]

After

derived = [[[22, 12, 11, 3], [22, 35, 34, 3], [45, 12, 33, 2], [45, 35, 10, 2]], [2, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S354





S356 · impliesBefore

source roles = [15, 5, [22, 45], [13, 36]]

After

derived = [[[22, 13, 12, 4], [22, 36, 35, 4], [45, 13, 32, 22], [45, 36, 9, 22]], [4, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S355





S357 · impliesBefore

source roles = [15, 6, [22, 45], [14, 37]]

After

derived = [[[22, 14, 13, 5], [22, 37, 36, 5], [45, 14, 31, 21], [45, 37, 8, 21]], [5, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S356





S358 · impliesBefore

source roles = [15, 7, [22, 45], [15, 38]]

After

derived = [[[22, 15, 14, 6], [22, 38, 37, 6], [45, 15, 30, 20], [45, 38, 7, 20]], [6, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S357





S359 · impliesBefore

source roles = [15, 8, [22, 45], [16, 39]]

After

derived = [[[22, 16, 15, 7], [22, 39, 38, 7], [45, 16, 29, 19], [45, 39, 6, 19]], [7, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S358





S360 · impliesBefore

source roles = [15, 9, [22, 45], [17, 40]]

After

derived = [[[22, 17, 16, 8], [22, 40, 39, 8], [45, 17, 28, 18], [45, 40, 5, 18]], [8, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S359





S361 · impliesBefore

source roles = [15, 10, [22, 45], [18, 41]]

After

derived = [[[22, 18, 17, 9], [22, 41, 40, 9], [45, 18, 27, 17], [45, 41, 4, 17]], [9, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S360





S362 · impliesBefore

source roles = [15, 11, [22, 45], [19, 42]]

After

derived = [[[22, 19, 18, 10], [22, 42, 41, 10], [45, 19, 26, 16], [45, 42, 3, 16]], [10, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S361





S363 · impliesBefore

source roles = [15, 12, [22, 45], [2, 25]]

After

derived = [[[22, 2, 1, 1], [22, 25, 24, 1], [45, 2, 43, 13], [45, 25, 20, 13]], [1, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S362





S364 · impliesBefore

source roles = [15, 13, [22, 45], [20, 43]]

After

derived = [[[22, 20, 19, 11], [22, 43, 42, 11], [45, 20, 25, 12], [45, 43, 2, 12]], [11, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S363





S365 · impliesBefore

source roles = [15, 14, [22, 45], [21, 44]]

After

derived = [[[22, 21, 20, 13], [22, 44, 43, 13], [45, 21, 24, 1], [45, 44, 1, 1]], [1, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S364





S366 · impliesBefore

source roles = [15, 15, [22, 45], [22, 45]]

After

derived = [[[22, 22, 21, 14], [22, 45, 44, 14], [45, 22, 23, 0], [45, 45, 0, 0]], [0, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S365





S367 · impliesBefore

source roles = [15, 16, [22, 45], [3, 26]]

After

derived = [[[22, 3, 2, 12], [22, 26, 25, 12], [45, 3, 42, 11], [45, 26, 19, 11]], [11, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S366





S368 · impliesBefore

source roles = [15, 17, [22, 45], [4, 27]]

After

derived = [[[22, 4, 3, 16], [22, 27, 26, 16], [45, 4, 41, 10], [45, 27, 18, 10]], [10, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S367





S369 · impliesBefore

source roles = [15, 18, [22, 45], [5, 28]]

After

derived = [[[22, 5, 4, 17], [22, 28, 27, 17], [45, 5, 40, 9], [45, 28, 17, 9]], [9, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S368





S370 · impliesBefore

source roles = [15, 19, [22, 45], [6, 29]]

After

derived = [[[22, 6, 5, 18], [22, 29, 28, 18], [45, 6, 39, 8], [45, 29, 16, 8]], [8, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S369





S371 · impliesBefore

source roles = [15, 20, [22, 45], [7, 30]]

After

derived = [[[22, 7, 6, 19], [22, 30, 29, 19], [45, 7, 38, 7], [45, 30, 15, 7]], [7, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S370





S372 · impliesBefore

source roles = [15, 21, [22, 45], [8, 31]]

After

derived = [[[22, 8, 7, 20], [22, 31, 30, 20], [45, 8, 37, 6], [45, 31, 14, 6]], [6, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S371





S373 · impliesBefore

source roles = [15, 22, [22, 45], [9, 32]]

After

derived = [[[22, 9, 8, 21], [22, 32, 31, 21], [45, 9, 36, 5], [45, 32, 13, 5]], [5, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S372





S374 · impliesBefore

source roles = [16, 0, [3, 26], [0, 23]]

After

derived = [[[3, 0, 3, 16], [3, 23, 26, 16], [26, 0, 26, 16], [26, 23, 3, 16]], [16], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S373





S375 · impliesBefore

source roles = [16, 1, [3, 26], [1, 24]]

After

derived = [[[3, 1, 4, 17], [3, 24, 27, 17], [26, 1, 25, 12], [26, 24, 2, 12]], [12, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S374





S376 · impliesBefore

source roles = [16, 2, [3, 26], [10, 33]]

After

derived = [[[3, 10, 13, 5], [3, 33, 36, 5], [26, 10, 39, 8], [26, 33, 16, 8]], [5, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S375





S377 · impliesBefore

source roles = [16, 3, [3, 26], [11, 34]]

After

derived = [[[3, 11, 14, 6], [3, 34, 37, 6], [26, 11, 38, 7], [26, 34, 15, 7]], [6, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S376





S378 · impliesBefore

source roles = [16, 4, [3, 26], [12, 35]]

After

derived = [[[3, 12, 15, 7], [3, 35, 38, 7], [26, 12, 37, 6], [26, 35, 14, 6]], [6, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S377





S379 · impliesBefore

source roles = [16, 5, [3, 26], [13, 36]]

After

derived = [[[3, 13, 16, 8], [3, 36, 39, 8], [26, 13, 36, 5], [26, 36, 13, 5]], [5, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S378





S380 · impliesBefore

source roles = [16, 6, [3, 26], [14, 37]]

After

derived = [[[3, 14, 17, 9], [3, 37, 40, 9], [26, 14, 35, 4], [26, 37, 12, 4]], [4, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S379





S381 · impliesBefore

source roles = [16, 7, [3, 26], [15, 38]]

After

derived = [[[3, 15, 18, 10], [3, 38, 41, 10], [26, 15, 34, 3], [26, 38, 11, 3]], [3, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S380





S382 · impliesBefore

source roles = [16, 8, [3, 26], [16, 39]]

After

derived = [[[3, 16, 19, 11], [3, 39, 42, 11], [26, 16, 33, 2], [26, 39, 10, 2]], [2, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S381





S383 · impliesBefore

source roles = [16, 9, [3, 26], [17, 40]]

After

derived = [[[3, 17, 20, 13], [3, 40, 43, 13], [26, 17, 32, 22], [26, 40, 9, 22]], [13, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S382





S384 · impliesBefore

source roles = [16, 10, [3, 26], [18, 41]]

After

derived = [[[3, 18, 21, 14], [3, 41, 44, 14], [26, 18, 31, 21], [26, 41, 8, 21]], [14, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S383





S385 · impliesBefore

source roles = [16, 11, [3, 26], [19, 42]]

After

derived = [[[3, 19, 22, 15], [3, 42, 45, 15], [26, 19, 30, 20], [26, 42, 7, 20]], [15, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S384





S386 · impliesBefore

source roles = [16, 12, [3, 26], [2, 25]]

After

derived = [[[3, 2, 5, 18], [3, 25, 28, 18], [26, 2, 24, 1], [26, 25, 1, 1]], [1, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S385





S387 · impliesBefore

source roles = [16, 13, [3, 26], [20, 43]]

After

derived = [[[3, 20, 0, 0], [3, 43, 23, 0], [26, 20, 29, 19], [26, 43, 6, 19]], [0, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S386





S388 · impliesBefore

source roles = [16, 14, [3, 26], [21, 44]]

After

derived = [[[3, 21, 1, 1], [3, 44, 24, 1], [26, 21, 28, 18], [26, 44, 5, 18]], [1, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S387





S389 · impliesBefore

source roles = [16, 15, [3, 26], [22, 45]]

After

derived = [[[3, 22, 2, 12], [3, 45, 25, 12], [26, 22, 27, 17], [26, 45, 4, 17]], [12, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S388





S390 · impliesBefore

source roles = [16, 16, [3, 26], [3, 26]]

After

derived = [[[3, 3, 6, 19], [3, 26, 29, 19], [26, 3, 23, 0], [26, 26, 0, 0]], [0, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S389





S391 · impliesBefore

source roles = [16, 17, [3, 26], [4, 27]]

After

derived = [[[3, 4, 7, 20], [3, 27, 30, 20], [26, 4, 45, 15], [26, 27, 22, 15]], [15, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S390





S392 · impliesBefore

source roles = [16, 18, [3, 26], [5, 28]]

After

derived = [[[3, 5, 8, 21], [3, 28, 31, 21], [26, 5, 44, 14], [26, 28, 21, 14]], [14, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S391





S393 · impliesBefore

source roles = [16, 19, [3, 26], [6, 29]]

After

derived = [[[3, 6, 9, 22], [3, 29, 32, 22], [26, 6, 43, 13], [26, 29, 20, 13]], [13, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S392





S394 · impliesBefore

source roles = [16, 20, [3, 26], [7, 30]]

After

derived = [[[3, 7, 10, 2], [3, 30, 33, 2], [26, 7, 42, 11], [26, 30, 19, 11]], [2, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S393





S395 · impliesBefore

source roles = [16, 21, [3, 26], [8, 31]]

After

derived = [[[3, 8, 11, 3], [3, 31, 34, 3], [26, 8, 41, 10], [26, 31, 18, 10]], [3, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S394





S396 · impliesBefore

source roles = [16, 22, [3, 26], [9, 32]]

After

derived = [[[3, 9, 12, 4], [3, 32, 35, 4], [26, 9, 40, 9], [26, 32, 17, 9]], [4, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S395





S397 · impliesBefore

source roles = [17, 0, [4, 27], [0, 23]]

After

derived = [[[4, 0, 4, 17], [4, 23, 27, 17], [27, 0, 27, 17], [27, 23, 4, 17]], [17], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S396





S398 · impliesBefore

source roles = [17, 1, [4, 27], [1, 24]]

After

derived = [[[4, 1, 5, 18], [4, 24, 28, 18], [27, 1, 26, 16], [27, 24, 3, 16]], [16, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S397





S399 · impliesBefore

source roles = [17, 2, [4, 27], [10, 33]]

After

derived = [[[4, 10, 14, 6], [4, 33, 37, 6], [27, 10, 40, 9], [27, 33, 17, 9]], [6, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S398





S400 · impliesBefore

source roles = [17, 3, [4, 27], [11, 34]]

After

derived = [[[4, 11, 15, 7], [4, 34, 38, 7], [27, 11, 39, 8], [27, 34, 16, 8]], [7, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S399





S401 · impliesBefore

source roles = [17, 4, [4, 27], [12, 35]]

After

derived = [[[4, 12, 16, 8], [4, 35, 39, 8], [27, 12, 38, 7], [27, 35, 15, 7]], [7, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S400





S402 · impliesBefore

source roles = [17, 5, [4, 27], [13, 36]]

After

derived = [[[4, 13, 17, 9], [4, 36, 40, 9], [27, 13, 37, 6], [27, 36, 14, 6]], [6, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S401





S403 · impliesBefore

source roles = [17, 6, [4, 27], [14, 37]]

After

derived = [[[4, 14, 18, 10], [4, 37, 41, 10], [27, 14, 36, 5], [27, 37, 13, 5]], [5, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S402





S404 · impliesBefore

source roles = [17, 7, [4, 27], [15, 38]]

After

derived = [[[4, 15, 19, 11], [4, 38, 42, 11], [27, 15, 35, 4], [27, 38, 12, 4]], [4, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S403





S405 · impliesBefore

source roles = [17, 8, [4, 27], [16, 39]]

After

derived = [[[4, 16, 20, 13], [4, 39, 43, 13], [27, 16, 34, 3], [27, 39, 11, 3]], [3, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S404





S406 · impliesBefore

source roles = [17, 9, [4, 27], [17, 40]]

After

derived = [[[4, 17, 21, 14], [4, 40, 44, 14], [27, 17, 33, 2], [27, 40, 10, 2]], [2, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S405





S407 · impliesBefore

source roles = [17, 10, [4, 27], [18, 41]]

After

derived = [[[4, 18, 22, 15], [4, 41, 45, 15], [27, 18, 32, 22], [27, 41, 9, 22]], [15, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S406





S408 · impliesBefore

source roles = [17, 11, [4, 27], [19, 42]]

After

derived = [[[4, 19, 0, 0], [4, 42, 23, 0], [27, 19, 31, 21], [27, 42, 8, 21]], [0, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S407





S409 · impliesBefore

source roles = [17, 12, [4, 27], [2, 25]]

After

derived = [[[4, 2, 6, 19], [4, 25, 29, 19], [27, 2, 25, 12], [27, 25, 2, 12]], [12, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S408





S410 · impliesBefore

source roles = [17, 13, [4, 27], [20, 43]]

After

derived = [[[4, 20, 1, 1], [4, 43, 24, 1], [27, 20, 30, 20], [27, 43, 7, 20]], [1, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S409





S411 · impliesBefore

source roles = [17, 14, [4, 27], [21, 44]]

After

derived = [[[4, 21, 2, 12], [4, 44, 25, 12], [27, 21, 29, 19], [27, 44, 6, 19]], [12, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S410





S412 · impliesBefore

source roles = [17, 15, [4, 27], [22, 45]]

After

derived = [[[4, 22, 3, 16], [4, 45, 26, 16], [27, 22, 28, 18], [27, 45, 5, 18]], [16, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S411





S413 · impliesBefore

source roles = [17, 16, [4, 27], [3, 26]]

After

derived = [[[4, 3, 7, 20], [4, 26, 30, 20], [27, 3, 24, 1], [27, 26, 1, 1]], [1, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S412





S414 · impliesBefore

source roles = [17, 17, [4, 27], [4, 27]]

After

derived = [[[4, 4, 8, 21], [4, 27, 31, 21], [27, 4, 23, 0], [27, 27, 0, 0]], [0, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S413





S415 · impliesBefore

source roles = [17, 18, [4, 27], [5, 28]]

After

derived = [[[4, 5, 9, 22], [4, 28, 32, 22], [27, 5, 45, 15], [27, 28, 22, 15]], [15, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S414





S416 · impliesBefore

source roles = [17, 19, [4, 27], [6, 29]]

After

derived = [[[4, 6, 10, 2], [4, 29, 33, 2], [27, 6, 44, 14], [27, 29, 21, 14]], [2, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S415





S417 · impliesBefore

source roles = [17, 20, [4, 27], [7, 30]]

After

derived = [[[4, 7, 11, 3], [4, 30, 34, 3], [27, 7, 43, 13], [27, 30, 20, 13]], [3, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S416





S418 · impliesBefore

source roles = [17, 21, [4, 27], [8, 31]]

After

derived = [[[4, 8, 12, 4], [4, 31, 35, 4], [27, 8, 42, 11], [27, 31, 19, 11]], [4, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S417





S419 · impliesBefore

source roles = [17, 22, [4, 27], [9, 32]]

After

derived = [[[4, 9, 13, 5], [4, 32, 36, 5], [27, 9, 41, 10], [27, 32, 18, 10]], [5, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S418





S420 · impliesBefore

source roles = [18, 0, [5, 28], [0, 23]]

After

derived = [[[5, 0, 5, 18], [5, 23, 28, 18], [28, 0, 28, 18], [28, 23, 5, 18]], [18], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S419





S421 · impliesBefore

source roles = [18, 1, [5, 28], [1, 24]]

After

derived = [[[5, 1, 6, 19], [5, 24, 29, 19], [28, 1, 27, 17], [28, 24, 4, 17]], [17, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S420





S422 · impliesBefore

source roles = [18, 2, [5, 28], [10, 33]]

After

derived = [[[5, 10, 15, 7], [5, 33, 38, 7], [28, 10, 41, 10], [28, 33, 18, 10]], [7, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S421





S423 · impliesBefore

source roles = [18, 3, [5, 28], [11, 34]]

After

derived = [[[5, 11, 16, 8], [5, 34, 39, 8], [28, 11, 40, 9], [28, 34, 17, 9]], [8, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S422





S424 · impliesBefore

source roles = [18, 4, [5, 28], [12, 35]]

After

derived = [[[5, 12, 17, 9], [5, 35, 40, 9], [28, 12, 39, 8], [28, 35, 16, 8]], [8, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S423





S425 · impliesBefore

source roles = [18, 5, [5, 28], [13, 36]]

After

derived = [[[5, 13, 18, 10], [5, 36, 41, 10], [28, 13, 38, 7], [28, 36, 15, 7]], [7, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S424





S426 · impliesBefore

source roles = [18, 6, [5, 28], [14, 37]]

After

derived = [[[5, 14, 19, 11], [5, 37, 42, 11], [28, 14, 37, 6], [28, 37, 14, 6]], [6, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S425





S427 · impliesBefore

source roles = [18, 7, [5, 28], [15, 38]]

After

derived = [[[5, 15, 20, 13], [5, 38, 43, 13], [28, 15, 36, 5], [28, 38, 13, 5]], [5, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S426





S428 · impliesBefore

source roles = [18, 8, [5, 28], [16, 39]]

After

derived = [[[5, 16, 21, 14], [5, 39, 44, 14], [28, 16, 35, 4], [28, 39, 12, 4]], [4, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S427





S429 · impliesBefore

source roles = [18, 9, [5, 28], [17, 40]]

After

derived = [[[5, 17, 22, 15], [5, 40, 45, 15], [28, 17, 34, 3], [28, 40, 11, 3]], [3, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S428





S430 · impliesBefore

source roles = [18, 10, [5, 28], [18, 41]]

After

derived = [[[5, 18, 0, 0], [5, 41, 23, 0], [28, 18, 33, 2], [28, 41, 10, 2]], [0, 2], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S429





S431 · impliesBefore

source roles = [18, 11, [5, 28], [19, 42]]

After

derived = [[[5, 19, 1, 1], [5, 42, 24, 1], [28, 19, 32, 22], [28, 42, 9, 22]], [1, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S430





S432 · impliesBefore

source roles = [18, 12, [5, 28], [2, 25]]

After

derived = [[[5, 2, 7, 20], [5, 25, 30, 20], [28, 2, 26, 16], [28, 25, 3, 16]], [16, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S431





S433 · impliesBefore

source roles = [18, 13, [5, 28], [20, 43]]

After

derived = [[[5, 20, 2, 12], [5, 43, 25, 12], [28, 20, 31, 21], [28, 43, 8, 21]], [12, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S432





S434 · impliesBefore

source roles = [18, 14, [5, 28], [21, 44]]

After

derived = [[[5, 21, 3, 16], [5, 44, 26, 16], [28, 21, 30, 20], [28, 44, 7, 20]], [16, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S433





S435 · impliesBefore

source roles = [18, 15, [5, 28], [22, 45]]

After

derived = [[[5, 22, 4, 17], [5, 45, 27, 17], [28, 22, 29, 19], [28, 45, 6, 19]], [17, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S434





S436 · impliesBefore

source roles = [18, 16, [5, 28], [3, 26]]

After

derived = [[[5, 3, 8, 21], [5, 26, 31, 21], [28, 3, 25, 12], [28, 26, 2, 12]], [12, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S435





S437 · impliesBefore

source roles = [18, 17, [5, 28], [4, 27]]

After

derived = [[[5, 4, 9, 22], [5, 27, 32, 22], [28, 4, 24, 1], [28, 27, 1, 1]], [1, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S436





S438 · impliesBefore

source roles = [18, 18, [5, 28], [5, 28]]

After

derived = [[[5, 5, 10, 2], [5, 28, 33, 2], [28, 5, 23, 0], [28, 28, 0, 0]], [0, 2], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S437





S439 · impliesBefore

source roles = [18, 19, [5, 28], [6, 29]]

After

derived = [[[5, 6, 11, 3], [5, 29, 34, 3], [28, 6, 45, 15], [28, 29, 22, 15]], [3, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S438





S440 · impliesBefore

source roles = [18, 20, [5, 28], [7, 30]]

After

derived = [[[5, 7, 12, 4], [5, 30, 35, 4], [28, 7, 44, 14], [28, 30, 21, 14]], [4, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S439





S441 · impliesBefore

source roles = [18, 21, [5, 28], [8, 31]]

After

derived = [[[5, 8, 13, 5], [5, 31, 36, 5], [28, 8, 43, 13], [28, 31, 20, 13]], [5, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S440





S442 · impliesBefore

source roles = [18, 22, [5, 28], [9, 32]]

After

derived = [[[5, 9, 14, 6], [5, 32, 37, 6], [28, 9, 42, 11], [28, 32, 19, 11]], [6, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S441





S443 · impliesBefore

source roles = [19, 0, [6, 29], [0, 23]]

After

derived = [[[6, 0, 6, 19], [6, 23, 29, 19], [29, 0, 29, 19], [29, 23, 6, 19]], [19], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S442





S444 · impliesBefore

source roles = [19, 1, [6, 29], [1, 24]]

After

derived = [[[6, 1, 7, 20], [6, 24, 30, 20], [29, 1, 28, 18], [29, 24, 5, 18]], [18, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S443





S445 · impliesBefore

source roles = [19, 2, [6, 29], [10, 33]]

After

derived = [[[6, 10, 16, 8], [6, 33, 39, 8], [29, 10, 42, 11], [29, 33, 19, 11]], [8, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S444





S446 · impliesBefore

source roles = [19, 3, [6, 29], [11, 34]]

After

derived = [[[6, 11, 17, 9], [6, 34, 40, 9], [29, 11, 41, 10], [29, 34, 18, 10]], [9, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S445





S447 · impliesBefore

source roles = [19, 4, [6, 29], [12, 35]]

After

derived = [[[6, 12, 18, 10], [6, 35, 41, 10], [29, 12, 40, 9], [29, 35, 17, 9]], [9, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S446





S448 · impliesBefore

source roles = [19, 5, [6, 29], [13, 36]]

After

derived = [[[6, 13, 19, 11], [6, 36, 42, 11], [29, 13, 39, 8], [29, 36, 16, 8]], [8, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S447





S449 · impliesBefore

source roles = [19, 6, [6, 29], [14, 37]]

After

derived = [[[6, 14, 20, 13], [6, 37, 43, 13], [29, 14, 38, 7], [29, 37, 15, 7]], [7, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S448





S450 · impliesBefore

source roles = [19, 7, [6, 29], [15, 38]]

After

derived = [[[6, 15, 21, 14], [6, 38, 44, 14], [29, 15, 37, 6], [29, 38, 14, 6]], [6, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S449





S451 · impliesBefore

source roles = [19, 8, [6, 29], [16, 39]]

After

derived = [[[6, 16, 22, 15], [6, 39, 45, 15], [29, 16, 36, 5], [29, 39, 13, 5]], [5, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S450





S452 · impliesBefore

source roles = [19, 9, [6, 29], [17, 40]]

After

derived = [[[6, 17, 0, 0], [6, 40, 23, 0], [29, 17, 35, 4], [29, 40, 12, 4]], [0, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S451





S453 · impliesBefore

source roles = [19, 10, [6, 29], [18, 41]]

After

derived = [[[6, 18, 1, 1], [6, 41, 24, 1], [29, 18, 34, 3], [29, 41, 11, 3]], [1, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S452





S454 · impliesBefore

source roles = [19, 11, [6, 29], [19, 42]]

After

derived = [[[6, 19, 2, 12], [6, 42, 25, 12], [29, 19, 33, 2], [29, 42, 10, 2]], [2, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S453





S455 · impliesBefore

source roles = [19, 12, [6, 29], [2, 25]]

After

derived = [[[6, 2, 8, 21], [6, 25, 31, 21], [29, 2, 27, 17], [29, 25, 4, 17]], [17, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S454





S456 · impliesBefore

source roles = [19, 13, [6, 29], [20, 43]]

After

derived = [[[6, 20, 3, 16], [6, 43, 26, 16], [29, 20, 32, 22], [29, 43, 9, 22]], [16, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S455





S457 · impliesBefore

source roles = [19, 14, [6, 29], [21, 44]]

After

derived = [[[6, 21, 4, 17], [6, 44, 27, 17], [29, 21, 31, 21], [29, 44, 8, 21]], [17, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S456





S458 · impliesBefore

source roles = [19, 15, [6, 29], [22, 45]]

After

derived = [[[6, 22, 5, 18], [6, 45, 28, 18], [29, 22, 30, 20], [29, 45, 7, 20]], [18, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S457





S459 · impliesBefore

source roles = [19, 16, [6, 29], [3, 26]]

After

derived = [[[6, 3, 9, 22], [6, 26, 32, 22], [29, 3, 26, 16], [29, 26, 3, 16]], [16, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S458





S460 · impliesBefore

source roles = [19, 17, [6, 29], [4, 27]]

After

derived = [[[6, 4, 10, 2], [6, 27, 33, 2], [29, 4, 25, 12], [29, 27, 2, 12]], [2, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S459





S461 · impliesBefore

source roles = [19, 18, [6, 29], [5, 28]]

After

derived = [[[6, 5, 11, 3], [6, 28, 34, 3], [29, 5, 24, 1], [29, 28, 1, 1]], [1, 3], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S460





S462 · impliesBefore

source roles = [19, 19, [6, 29], [6, 29]]

After

derived = [[[6, 6, 12, 4], [6, 29, 35, 4], [29, 6, 23, 0], [29, 29, 0, 0]], [0, 4], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S461





S463 · impliesBefore

source roles = [19, 20, [6, 29], [7, 30]]

After

derived = [[[6, 7, 13, 5], [6, 30, 36, 5], [29, 7, 45, 15], [29, 30, 22, 15]], [5, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S462





S464 · impliesBefore

source roles = [19, 21, [6, 29], [8, 31]]

After

derived = [[[6, 8, 14, 6], [6, 31, 37, 6], [29, 8, 44, 14], [29, 31, 21, 14]], [6, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S463





S465 · impliesBefore

source roles = [19, 22, [6, 29], [9, 32]]

After

derived = [[[6, 9, 15, 7], [6, 32, 38, 7], [29, 9, 43, 13], [29, 32, 20, 13]], [7, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S464





S466 · impliesBefore

source roles = [20, 0, [7, 30], [0, 23]]

After

derived = [[[7, 0, 7, 20], [7, 23, 30, 20], [30, 0, 30, 20], [30, 23, 7, 20]], [20], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S465





S467 · impliesBefore

source roles = [20, 1, [7, 30], [1, 24]]

After

derived = [[[7, 1, 8, 21], [7, 24, 31, 21], [30, 1, 29, 19], [30, 24, 6, 19]], [19, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S466





S468 · impliesBefore

source roles = [20, 2, [7, 30], [10, 33]]

After

derived = [[[7, 10, 17, 9], [7, 33, 40, 9], [30, 10, 43, 13], [30, 33, 20, 13]], [9, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S467





S469 · impliesBefore

source roles = [20, 3, [7, 30], [11, 34]]

After

derived = [[[7, 11, 18, 10], [7, 34, 41, 10], [30, 11, 42, 11], [30, 34, 19, 11]], [10, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S468





S470 · impliesBefore

source roles = [20, 4, [7, 30], [12, 35]]

After

derived = [[[7, 12, 19, 11], [7, 35, 42, 11], [30, 12, 41, 10], [30, 35, 18, 10]], [10, 11], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S469





S471 · impliesBefore

source roles = [20, 5, [7, 30], [13, 36]]

After

derived = [[[7, 13, 20, 13], [7, 36, 43, 13], [30, 13, 40, 9], [30, 36, 17, 9]], [9, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S470





S472 · impliesBefore

source roles = [20, 6, [7, 30], [14, 37]]

After

derived = [[[7, 14, 21, 14], [7, 37, 44, 14], [30, 14, 39, 8], [30, 37, 16, 8]], [8, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S471





S473 · impliesBefore

source roles = [20, 7, [7, 30], [15, 38]]

After

derived = [[[7, 15, 22, 15], [7, 38, 45, 15], [30, 15, 38, 7], [30, 38, 15, 7]], [7, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S472





S474 · impliesBefore

source roles = [20, 8, [7, 30], [16, 39]]

After

derived = [[[7, 16, 0, 0], [7, 39, 23, 0], [30, 16, 37, 6], [30, 39, 14, 6]], [0, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S473





S475 · impliesBefore

source roles = [20, 9, [7, 30], [17, 40]]

After

derived = [[[7, 17, 1, 1], [7, 40, 24, 1], [30, 17, 36, 5], [30, 40, 13, 5]], [1, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S474





S476 · impliesBefore

source roles = [20, 10, [7, 30], [18, 41]]

After

derived = [[[7, 18, 2, 12], [7, 41, 25, 12], [30, 18, 35, 4], [30, 41, 12, 4]], [4, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S475





S477 · impliesBefore

source roles = [20, 11, [7, 30], [19, 42]]

After

derived = [[[7, 19, 3, 16], [7, 42, 26, 16], [30, 19, 34, 3], [30, 42, 11, 3]], [3, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S476





S478 · impliesBefore

source roles = [20, 12, [7, 30], [2, 25]]

After

derived = [[[7, 2, 9, 22], [7, 25, 32, 22], [30, 2, 28, 18], [30, 25, 5, 18]], [18, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S477





S479 · impliesBefore

source roles = [20, 13, [7, 30], [20, 43]]

After

derived = [[[7, 20, 4, 17], [7, 43, 27, 17], [30, 20, 33, 2], [30, 43, 10, 2]], [2, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S478





S480 · impliesBefore

source roles = [20, 14, [7, 30], [21, 44]]

After

derived = [[[7, 21, 5, 18], [7, 44, 28, 18], [30, 21, 32, 22], [30, 44, 9, 22]], [18, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S479





S481 · impliesBefore

source roles = [20, 15, [7, 30], [22, 45]]

After

derived = [[[7, 22, 6, 19], [7, 45, 29, 19], [30, 22, 31, 21], [30, 45, 8, 21]], [19, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S480





S482 · impliesBefore

source roles = [20, 16, [7, 30], [3, 26]]

After

derived = [[[7, 3, 10, 2], [7, 26, 33, 2], [30, 3, 27, 17], [30, 26, 4, 17]], [2, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S481





S483 · impliesBefore

source roles = [20, 17, [7, 30], [4, 27]]

After

derived = [[[7, 4, 11, 3], [7, 27, 34, 3], [30, 4, 26, 16], [30, 27, 3, 16]], [3, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S482





S484 · impliesBefore

source roles = [20, 18, [7, 30], [5, 28]]

After

derived = [[[7, 5, 12, 4], [7, 28, 35, 4], [30, 5, 25, 12], [30, 28, 2, 12]], [4, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S483





S485 · impliesBefore

source roles = [20, 19, [7, 30], [6, 29]]

After

derived = [[[7, 6, 13, 5], [7, 29, 36, 5], [30, 6, 24, 1], [30, 29, 1, 1]], [1, 5], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S484





S486 · impliesBefore

source roles = [20, 20, [7, 30], [7, 30]]

After

derived = [[[7, 7, 14, 6], [7, 30, 37, 6], [30, 7, 23, 0], [30, 30, 0, 0]], [0, 6], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S485





S487 · impliesBefore

source roles = [20, 21, [7, 30], [8, 31]]

After

derived = [[[7, 8, 15, 7], [7, 31, 38, 7], [30, 8, 45, 15], [30, 31, 22, 15]], [7, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S486





S488 · impliesBefore

source roles = [20, 22, [7, 30], [9, 32]]

After

derived = [[[7, 9, 16, 8], [7, 32, 39, 8], [30, 9, 44, 14], [30, 32, 21, 14]], [8, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S487





S489 · impliesBefore

source roles = [21, 0, [8, 31], [0, 23]]

After

derived = [[[8, 0, 8, 21], [8, 23, 31, 21], [31, 0, 31, 21], [31, 23, 8, 21]], [21], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S488





S490 · impliesBefore

source roles = [21, 1, [8, 31], [1, 24]]

After

derived = [[[8, 1, 9, 22], [8, 24, 32, 22], [31, 1, 30, 20], [31, 24, 7, 20]], [20, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S489





S491 · impliesBefore

source roles = [21, 2, [8, 31], [10, 33]]

After

derived = [[[8, 10, 18, 10], [8, 33, 41, 10], [31, 10, 44, 14], [31, 33, 21, 14]], [10, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S490





S492 · impliesBefore

source roles = [21, 3, [8, 31], [11, 34]]

After

derived = [[[8, 11, 19, 11], [8, 34, 42, 11], [31, 11, 43, 13], [31, 34, 20, 13]], [11, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S491





S493 · impliesBefore

source roles = [21, 4, [8, 31], [12, 35]]

After

derived = [[[8, 12, 20, 13], [8, 35, 43, 13], [31, 12, 42, 11], [31, 35, 19, 11]], [11, 13], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S492





S494 · impliesBefore

source roles = [21, 5, [8, 31], [13, 36]]

After

derived = [[[8, 13, 21, 14], [8, 36, 44, 14], [31, 13, 41, 10], [31, 36, 18, 10]], [10, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S493





S495 · impliesBefore

source roles = [21, 6, [8, 31], [14, 37]]

After

derived = [[[8, 14, 22, 15], [8, 37, 45, 15], [31, 14, 40, 9], [31, 37, 17, 9]], [9, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S494





S496 · impliesBefore

source roles = [21, 7, [8, 31], [15, 38]]

After

derived = [[[8, 15, 0, 0], [8, 38, 23, 0], [31, 15, 39, 8], [31, 38, 16, 8]], [0, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S495





S497 · impliesBefore

source roles = [21, 8, [8, 31], [16, 39]]

After

derived = [[[8, 16, 1, 1], [8, 39, 24, 1], [31, 16, 38, 7], [31, 39, 15, 7]], [1, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S496





S498 · impliesBefore

source roles = [21, 9, [8, 31], [17, 40]]

After

derived = [[[8, 17, 2, 12], [8, 40, 25, 12], [31, 17, 37, 6], [31, 40, 14, 6]], [6, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S497





S499 · impliesBefore

source roles = [21, 10, [8, 31], [18, 41]]

After

derived = [[[8, 18, 3, 16], [8, 41, 26, 16], [31, 18, 36, 5], [31, 41, 13, 5]], [5, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S498





S500 · impliesBefore

source roles = [21, 11, [8, 31], [19, 42]]

After

derived = [[[8, 19, 4, 17], [8, 42, 27, 17], [31, 19, 35, 4], [31, 42, 12, 4]], [4, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S499





S501 · impliesBefore

source roles = [21, 12, [8, 31], [2, 25]]

After

derived = [[[8, 2, 10, 2], [8, 25, 33, 2], [31, 2, 29, 19], [31, 25, 6, 19]], [2, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S500





S502 · impliesBefore

source roles = [21, 13, [8, 31], [20, 43]]

After

derived = [[[8, 20, 5, 18], [8, 43, 28, 18], [31, 20, 34, 3], [31, 43, 11, 3]], [3, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S501





S503 · impliesBefore

source roles = [21, 14, [8, 31], [21, 44]]

After

derived = [[[8, 21, 6, 19], [8, 44, 29, 19], [31, 21, 33, 2], [31, 44, 10, 2]], [2, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S502





S504 · impliesBefore

source roles = [21, 15, [8, 31], [22, 45]]

After

derived = [[[8, 22, 7, 20], [8, 45, 30, 20], [31, 22, 32, 22], [31, 45, 9, 22]], [20, 22], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S503





S505 · impliesBefore

source roles = [21, 16, [8, 31], [3, 26]]

After

derived = [[[8, 3, 11, 3], [8, 26, 34, 3], [31, 3, 28, 18], [31, 26, 5, 18]], [3, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S504





S506 · impliesBefore

source roles = [21, 17, [8, 31], [4, 27]]

After

derived = [[[8, 4, 12, 4], [8, 27, 35, 4], [31, 4, 27, 17], [31, 27, 4, 17]], [4, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S505





S507 · impliesBefore

source roles = [21, 18, [8, 31], [5, 28]]

After

derived = [[[8, 5, 13, 5], [8, 28, 36, 5], [31, 5, 26, 16], [31, 28, 3, 16]], [5, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S506





S508 · impliesBefore

source roles = [21, 19, [8, 31], [6, 29]]

After

derived = [[[8, 6, 14, 6], [8, 29, 37, 6], [31, 6, 25, 12], [31, 29, 2, 12]], [6, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S507





S509 · impliesBefore

source roles = [21, 20, [8, 31], [7, 30]]

After

derived = [[[8, 7, 15, 7], [8, 30, 38, 7], [31, 7, 24, 1], [31, 30, 1, 1]], [1, 7], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S508





S510 · impliesBefore

source roles = [21, 21, [8, 31], [8, 31]]

After

derived = [[[8, 8, 16, 8], [8, 31, 39, 8], [31, 8, 23, 0], [31, 31, 0, 0]], [0, 8], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S509





S511 · impliesBefore

source roles = [21, 22, [8, 31], [9, 32]]

After

derived = [[[8, 9, 17, 9], [8, 32, 40, 9], [31, 9, 45, 15], [31, 32, 22, 15]], [9, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S510





S512 · impliesBefore

source roles = [22, 0, [9, 32], [0, 23]]

After

derived = [[[9, 0, 9, 22], [9, 23, 32, 22], [32, 0, 32, 22], [32, 23, 9, 22]], [22], 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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S511





S513 · impliesBefore

source roles = [22, 1, [9, 32], [1, 24]]

After

derived = [[[9, 1, 10, 2], [9, 24, 33, 2], [32, 1, 31, 21], [32, 24, 8, 21]], [2, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S512





S514 · impliesBefore

source roles = [22, 2, [9, 32], [10, 33]]

After

derived = [[[9, 10, 19, 11], [9, 33, 42, 11], [32, 10, 45, 15], [32, 33, 22, 15]], [11, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S513





S515 · impliesBefore

source roles = [22, 3, [9, 32], [11, 34]]

After

derived = [[[9, 11, 20, 13], [9, 34, 43, 13], [32, 11, 44, 14], [32, 34, 21, 14]], [13, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S514





S516 · impliesBefore

source roles = [22, 4, [9, 32], [12, 35]]

After

derived = [[[9, 12, 21, 14], [9, 35, 44, 14], [32, 12, 43, 13], [32, 35, 20, 13]], [13, 14], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S515





S517 · impliesBefore

source roles = [22, 5, [9, 32], [13, 36]]

After

derived = [[[9, 13, 22, 15], [9, 36, 45, 15], [32, 13, 42, 11], [32, 36, 19, 11]], [11, 15], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S516





S518 · impliesBefore

source roles = [22, 6, [9, 32], [14, 37]]

After

derived = [[[9, 14, 0, 0], [9, 37, 23, 0], [32, 14, 41, 10], [32, 37, 18, 10]], [0, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S517





S519 · impliesBefore

source roles = [22, 7, [9, 32], [15, 38]]

After

derived = [[[9, 15, 1, 1], [9, 38, 24, 1], [32, 15, 40, 9], [32, 38, 17, 9]], [1, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S518





S520 · impliesBefore

source roles = [22, 8, [9, 32], [16, 39]]

After

derived = [[[9, 16, 2, 12], [9, 39, 25, 12], [32, 16, 39, 8], [32, 39, 16, 8]], [8, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S519





S521 · impliesBefore

source roles = [22, 9, [9, 32], [17, 40]]

After

derived = [[[9, 17, 3, 16], [9, 40, 26, 16], [32, 17, 38, 7], [32, 40, 15, 7]], [7, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S520





S522 · impliesBefore

source roles = [22, 10, [9, 32], [18, 41]]

After

derived = [[[9, 18, 4, 17], [9, 41, 27, 17], [32, 18, 37, 6], [32, 41, 14, 6]], [6, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S521





S523 · impliesBefore

source roles = [22, 11, [9, 32], [19, 42]]

After

derived = [[[9, 19, 5, 18], [9, 42, 28, 18], [32, 19, 36, 5], [32, 42, 13, 5]], [5, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S522





S524 · impliesBefore

source roles = [22, 12, [9, 32], [2, 25]]

After

derived = [[[9, 2, 11, 3], [9, 25, 34, 3], [32, 2, 30, 20], [32, 25, 7, 20]], [3, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S523





S525 · impliesBefore

source roles = [22, 13, [9, 32], [20, 43]]

After

derived = [[[9, 20, 6, 19], [9, 43, 29, 19], [32, 20, 35, 4], [32, 43, 12, 4]], [4, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S524





S526 · impliesBefore

source roles = [22, 14, [9, 32], [21, 44]]

After

derived = [[[9, 21, 7, 20], [9, 44, 30, 20], [32, 21, 34, 3], [32, 44, 11, 3]], [3, 20], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S525





S527 · impliesBefore

source roles = [22, 15, [9, 32], [22, 45]]

After

derived = [[[9, 22, 8, 21], [9, 45, 31, 21], [32, 22, 33, 2], [32, 45, 10, 2]], [2, 21], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S526





S528 · impliesBefore

source roles = [22, 16, [9, 32], [3, 26]]

After

derived = [[[9, 3, 12, 4], [9, 26, 35, 4], [32, 3, 29, 19], [32, 26, 6, 19]], [4, 19], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S527





S529 · impliesBefore

source roles = [22, 17, [9, 32], [4, 27]]

After

derived = [[[9, 4, 13, 5], [9, 27, 36, 5], [32, 4, 28, 18], [32, 27, 5, 18]], [5, 18], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S528





S530 · impliesBefore

source roles = [22, 18, [9, 32], [5, 28]]

After

derived = [[[9, 5, 14, 6], [9, 28, 37, 6], [32, 5, 27, 17], [32, 28, 4, 17]], [6, 17], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S529





S531 · impliesBefore

source roles = [22, 19, [9, 32], [6, 29]]

After

derived = [[[9, 6, 15, 7], [9, 29, 38, 7], [32, 6, 26, 16], [32, 29, 3, 16]], [7, 16], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S530





S532 · impliesBefore

source roles = [22, 20, [9, 32], [7, 30]]

After

derived = [[[9, 7, 16, 8], [9, 30, 39, 8], [32, 7, 25, 12], [32, 30, 2, 12]], [8, 12], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S531





S533 · impliesBefore

source roles = [22, 21, [9, 32], [8, 31]]

After

derived = [[[9, 8, 17, 9], [9, 31, 40, 9], [32, 8, 24, 1], [32, 31, 1, 1]], [1, 9], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S532





S534 · impliesBefore

source roles = [22, 22, [9, 32], [9, 32]]

After

derived = [[[9, 9, 18, 10], [9, 32, 41, 10], [32, 9, 23, 0], [32, 32, 0, 0]], [0, 10], No]

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 dependenciesRule: Quotient_EVERY_coset_pair_ALL_representative_products · Uses: G001, S533





S535 · impliesBefore

source roles = [[0, 1, [1, 15], No], [0, 23], [1, 24]]

After

derived = [[0, 1, 0, 1, 1, 23, 1, 15], 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 dependenciesRule: Quotient_FIRST_bad_pair_exact_source_nested_representative_witness · Uses: G001, S534









## Reverse checks


- 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, 23], No, [[0, 23], [1, 24], [10, 33], [11, 34], [12, 35], [13, 36], [14, 37], [15, 38], [16, 39], [17, 40], [18, 41], [19, 42], [2, 25], [20, 43], [21, 44], [22, 45], [3, 26], [4, 27], [5, 28], [6, 29], [7, 30], [8, 31], [9, 32]], [0, 1, 0, 1, 1, 23, 1, 15], 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: 1319abc0f2ae91c5b87e128dcee8d38cc2e7e92e760f2b85b77a1435cce638e3
- candidate record SHA-256: 05abceff50e377b9e167ae5bcd16d8d4510a16efeae1b7ab365bbcc40518cf84
- semantic review receipt SHA-256: 6212b8b0b3b273f3a514e26ebd17d7e81219c56a8f47e40047ee2b6bf01d1ba3
- question-first witness SHA-256: f32a23d5e1b66c7794c60def58741bcdfacff24f3cdfc9bc48109c8f71543cf3
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r02-finite-quotient-group-0096.json)