Question 25737: First Isomorphism Reaches the Image, Not Automatically the Whole Codomain

Original question and givens

Use complete source Cayley table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]], identity=0, target table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [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, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 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]], identity=0, and the aligned total mapping=[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24]. Table row x/column y is x*y. Qualify both groups, then every homomorphism product pair before invoking the theorem. Give (image, codomain_order, image_order, surjective_to_codomain, image_isomorphism_statement, codomain_scope, general_theorem_proof_claim, boundary).

• G001 — Use complete source Cayley table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]], identity=0, target table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [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, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 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]], identity=0, and the aligned total mapping=[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24]. Table row x/column y is x*y. Qualify both groups, then every homomorphism product pair before invoking the theorem. Give (image, codomain_order, image_order, surjective_to_codomain, image_isomorphism_statement, codomain_scope, general_theorem_proof_claim, 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-first-isomorphism-theorem-finite-groups

Step-by-step derivation

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

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

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

derived = [13, [[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]], Yes]

source roles = [Iso1 ORIGINAL SOURCE, 13, 0]

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]], 2197, [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]

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

derived = [26, [[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]], Yes]

source roles = [Iso1 ORIGINAL TARGET, 26, 0]

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]], 17576, [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]

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

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

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

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

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

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

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

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

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

derived = [[[0, 0, 0, 0, Yes], [0, 1, 2, 2, Yes], [0, 2, 20, 20, Yes], [0, 3, 22, 22, Yes], [0, 4, 24, 24, Yes], [0, 5, 4, 4, Yes], [0, 6, 6, 6, Yes], [0, 7, 8, 8, Yes], [0, 8, 10, 10, Yes], [0, 9, 12, 12, Yes], [0, 10, 14, 14, Yes], [0, 11, 16, 16, Yes], [0, 12, 18, 18, Yes], [1, 0, 2, 2, Yes], [1, 1, 4, 4, Yes], [1, 2, 22, 22, Yes], [1, 3, 24, 24, Yes], [1, 4, 0, 0, Yes], [1, 5, 6, 6, Yes], [1, 6, 8, 8, Yes], [1, 7, 10, 10, Yes], [1, 8, 12, 12, Yes], [1, 9, 14, 14, Yes], [1, 10, 16, 16, Yes], [1, 11, 18, 18, Yes], [1, 12, 20, 20, Yes], [2, 0, 20, 20, Yes], [2, 1, 22, 22, Yes], [2, 2, 14, 14, Yes], [2, 3, 16, 16, Yes], [2, 4, 18, 18, Yes], [2, 5, 24, 24, Yes], [2, 6, 0, 0, Yes], [2, 7, 2, 2, Yes], [2, 8, 4, 4, Yes], [2, 9, 6, 6, Yes], [2, 10, 8, 8, Yes], [2, 11, 10, 10, Yes], [2, 12, 12, 12, Yes], [3, 0, 22, 22, Yes], [3, 1, 24, 24, Yes], [3, 2, 16, 16, Yes], [3, 3, 18, 18, Yes], [3, 4, 20, 20, Yes], [3, 5, 0, 0, Yes], [3, 6, 2, 2, Yes], [3, 7, 4, 4, Yes], [3, 8, 6, 6, Yes], [3, 9, 8, 8, Yes], [3, 10, 10, 10, Yes], [3, 11, 12, 12, Yes], [3, 12, 14, 14, Yes], [4, 0, 24, 24, Yes], [4, 1, 0, 0, Yes], [4, 2, 18, 18, Yes], [4, 3, 20, 20, Yes], [4, 4, 22, 22, Yes], [4, 5, 2, 2, Yes], [4, 6, 4, 4, Yes], [4, 7, 6, 6, Yes], [4, 8, 8, 8, Yes], [4, 9, 10, 10, Yes], [4, 10, 12, 12, Yes], [4, 11, 14, 14, Yes], [4, 12, 16, 16, Yes], [5, 0, 4, 4, Yes], [5, 1, 6, 6, Yes], [5, 2, 24, 24, Yes], [5, 3, 0, 0, Yes], [5, 4, 2, 2, Yes], [5, 5, 8, 8, Yes], [5, 6, 10, 10, Yes], [5, 7, 12, 12, Yes], [5, 8, 14, 14, Yes], [5, 9, 16, 16, Yes], [5, 10, 18, 18, Yes], [5, 11, 20, 20, Yes], [5, 12, 22, 22, Yes], [6, 0, 6, 6, Yes], [6, 1, 8, 8, Yes], [6, 2, 0, 0, Yes], [6, 3, 2, 2, Yes], [6, 4, 4, 4, Yes], [6, 5, 10, 10, Yes], [6, 6, 12, 12, Yes], [6, 7, 14, 14, Yes], [6, 8, 16, 16, Yes], [6, 9, 18, 18, Yes], [6, 10, 20, 20, Yes], [6, 11, 22, 22, Yes], [6, 12, 24, 24, Yes], [7, 0, 8, 8, Yes], [7, 1, 10, 10, Yes], [7, 2, 2, 2, Yes], [7, 3, 4, 4, Yes], [7, 4, 6, 6, Yes], [7, 5, 12, 12, Yes], [7, 6, 14, 14, Yes], [7, 7, 16, 16, Yes], [7, 8, 18, 18, Yes], [7, 9, 20, 20, Yes], [7, 10, 22, 22, Yes], [7, 11, 24, 24, Yes], [7, 12, 0, 0, Yes], [8, 0, 10, 10, Yes], [8, 1, 12, 12, Yes], [8, 2, 4, 4, Yes], [8, 3, 6, 6, Yes], [8, 4, 8, 8, Yes], [8, 5, 14, 14, Yes], [8, 6, 16, 16, Yes], [8, 7, 18, 18, Yes], [8, 8, 20, 20, Yes], [8, 9, 22, 22, Yes], [8, 10, 24, 24, Yes], [8, 11, 0, 0, Yes], [8, 12, 2, 2, Yes], [9, 0, 12, 12, Yes], [9, 1, 14, 14, Yes], [9, 2, 6, 6, Yes], [9, 3, 8, 8, Yes], [9, 4, 10, 10, Yes], [9, 5, 16, 16, Yes], [9, 6, 18, 18, Yes], [9, 7, 20, 20, Yes], [9, 8, 22, 22, Yes], [9, 9, 24, 24, Yes], [9, 10, 0, 0, Yes], [9, 11, 2, 2, Yes], [9, 12, 4, 4, Yes], [10, 0, 14, 14, Yes], [10, 1, 16, 16, Yes], [10, 2, 8, 8, Yes], [10, 3, 10, 10, Yes], [10, 4, 12, 12, Yes], [10, 5, 18, 18, Yes], [10, 6, 20, 20, Yes], [10, 7, 22, 22, Yes], [10, 8, 24, 24, Yes], [10, 9, 0, 0, Yes], [10, 10, 2, 2, Yes], [10, 11, 4, 4, Yes], [10, 12, 6, 6, Yes], [11, 0, 16, 16, Yes], [11, 1, 18, 18, Yes], [11, 2, 10, 10, Yes], [11, 3, 12, 12, Yes], [11, 4, 14, 14, Yes], [11, 5, 20, 20, Yes], [11, 6, 22, 22, Yes], [11, 7, 24, 24, Yes], [11, 8, 0, 0, Yes], [11, 9, 2, 2, Yes], [11, 10, 4, 4, Yes], [11, 11, 6, 6, Yes], [11, 12, 8, 8, Yes], [12, 0, 18, 18, Yes], [12, 1, 20, 20, Yes], [12, 2, 12, 12, Yes], [12, 3, 14, 14, Yes], [12, 4, 16, 16, Yes], [12, 5, 22, 22, Yes], [12, 6, 24, 24, Yes], [12, 7, 0, 0, Yes], [12, 8, 2, 2, Yes], [12, 9, 4, 4, Yes], [12, 10, 6, 6, Yes], [12, 11, 8, 8, Yes], [12, 12, 10, 10, Yes]], Yes, Yes, Yes, Yes, No]

source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24], 26, 13]

derived = [No, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, No]

Reverse checks

• 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, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24], 26, 13, No, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, No, finite_instance_certificate_not_a_general_theorem_proof)

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.