`offDiagEntries_eq`

proved

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module: IndisputableMonolith.CrossDomain.CrossPatternMatrix
domain: CrossDomain
line: 96 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.CrossPatternMatrix on GitHub at line 96.

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depends on

formal source

  93def offDiagSize : ℕ := 4
  94def offDiagEntries : ℕ := offDiagSize * offDiagSize
  95
  96theorem offDiagEntries_eq : offDiagEntries = 16 := by decide
  97
  98/-- 16 = 2⁴ (the off-diagonal entry count is a power of 2). -/
  99theorem offDiag_is_two_fourth : offDiagEntries = 2^4 := by decide
 100
 101structure CrossPatternMatrixCert where
 102  D5_squared : (5 : ℕ) * 5 = 25
 103  D5_2cube : (5 : ℕ) * 2^3 = 40
 104  twoCube_squared : (2 : ℕ)^3 * 2^3 = 64
 105  full_turn : (2 : ℕ)^3 * 45 = 360
 106  gap_squared : (45 : ℕ) * 45 = 2025
 107  cube_faces_squared : (6 : ℕ) * 6 = 36
 108  face_pairs_minus_gap_is_D_sq : (45 : ℕ) - 6 * 6 = 9
 109  off_diag_count : offDiagEntries = 2^4
 110
 111def crossPatternMatrixCert : CrossPatternMatrixCert where
 112  D5_squared := D5_squared
 113  D5_2cube := D5_times_2cube
 114  twoCube_squared := twoCube_squared
 115  full_turn := full_turn
 116  gap_squared := gap_squared
 117  cube_faces_squared := cube_faces_squared
 118  face_pairs_minus_gap_is_D_sq := face_pairs_minus_gap
 119  off_diag_count := offDiag_is_two_fourth
 120
 121end IndisputableMonolith.CrossDomain.CrossPatternMatrix

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