| import OAI.Analysis.GroupDeterminants.ProjectionCriterion | |
| namespace OAI | |
| noncomputable section | |
| open scoped BigOperators Pointwise | |
| namespace GroupRingDeterminant | |
| theorem main_of_companion_input (input : CompanionInput) : MainStatement := by | |
| obtain ⟨K, hK, hKfinite, hKchar, H, hH, hHfg, a, b, hab, hba⟩ := input | |
| let := hK | |
| let := hKfinite | |
| let := hKchar | |
| let := hH | |
| let := hHfg | |
| obtain ⟨d, hd, X, Y, hXY, hYX⟩ := binary_matrix_of_finite_field K H a b hab hba | |
| let : Nonempty (Fin d) := ⟨⟨0, by omega⟩⟩ | |
| obtain ⟨D, hD, P, hP, hPs, ht, Z, hZ, u, v, huv⟩ := lamp_projection_data X Y hXY hYX | |
| exact projection_criterion D hD P ⟨hP, hPs⟩ ht Z hZ u v huv | |
| end GroupRingDeterminant | |
| end | |
| end OAI | |