One zero fine coordinate kills a selected mixed-owner map

import Definitions.Def_mme_dwz_step1_mixed_common_state_source_data

open MME Module PiTensorProduct

universe u

set_option autoImplicit false

open MME.DWZSourceAligned
open MME.DWZStep1Support
open MME.DWZGlobalCorrelated

theorem mme_dwz_step1_filtered_mixed_selected_map_zero_of_coordinate
    {K : Type u} [Field K]
    (m : ℕ) {p N L n : ℕ}
    (reindex : Fin (N + 1) ≃ Fin L)
    (q : (Fin (N + 2) → ZMod p) × ZMod p)
    (edge : Fin n → Fin (N + 1) → Fin 15)
    (competitor owner : Fin n)
    (W : AddressZWord (sourceWord reindex edge owner))
    (x : AddressModeWord (sourceWord reindex edge competitor) 0)
    (y : AddressModeWord (sourceWord reindex edge competitor) 1)
    (r : Fin L)
    (hFineZero : (cwSquareFineSplitGrading K 6).blockTensor
      (fun i ↦ MME.DWZStep1Support.fineSplitGrade
        (![addressModeLeftGrade x r,
          addressModeLeftGrade y r,
          (W r).leftGrade] i)
        (![addressModeRightGrade x r,
          addressModeRightGrade y r,
          (W r).rightGrade] i)) = 0) :
    PiTensorProduct.map
      (step1FilteredMixedSelectedXYMaps K m reindex q edge
        competitor owner W x y)
      ((TensorObj.kron (CWObj K 6) (CWObj K 6)).kronPow L).t = 0 := by
  sorry