OAI/LinearAlgebra/MatrixMultiplication/FieldParameters/HalfLaws.lean

GitHub source file

26 declarations, 0 contain sorry, 0 declared as axioms

Fixed rational distributions and their entropy and capacity formulas.

  1. theorem OAI.MatrixMultiplication.AllFieldParameters.stageBLaw_nonnegative line 12
  2. theorem OAI.MatrixMultiplication.AllFieldParameters.orderedPairs_mem_iff line 17
  3. theorem OAI.MatrixMultiplication.AllFieldParameters.zeroPairLaw_nonnegative line 27
  4. theorem OAI.MatrixMultiplication.AllFieldParameters.zeroPairLaw_full_normalized line 34
  5. def OAI.MatrixMultiplication.AllFieldParameters.positiveHalfLaw line 49
  6. theorem OAI.MatrixMultiplication.AllFieldParameters.positiveHalfLaw_nonnegative line 53
  7. theorem OAI.MatrixMultiplication.AllFieldParameters.sum_pair_mixture line 61
  8. theorem OAI.MatrixMultiplication.AllFieldParameters.positiveHalfLaw_normalized line 78
  9. theorem OAI.MatrixMultiplication.AllFieldParameters.stageB_complement_permutation line 85
  10. theorem OAI.MatrixMultiplication.AllFieldParameters.stageB_complement_involution line 88
  11. theorem OAI.MatrixMultiplication.AllFieldParameters.positiveHalfLaw_swap line 93
  12. def OAI.MatrixMultiplication.AllFieldParameters.halfMaxAxis line 108
  13. def OAI.MatrixMultiplication.AllFieldParameters.halfLaw line 111
  14. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_positive_parent line 117
  15. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_swap line 122
  16. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_nonnegative line 136
  17. def OAI.MatrixMultiplication.AllFieldParameters.kappaEquiv line 146
  18. theorem OAI.MatrixMultiplication.AllFieldParameters.sum_pair_kappa line 152
  19. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_normalized line 156
  20. theorem OAI.MatrixMultiplication.AllFieldParameters.positiveHalfLaw_outside_support line 172
  21. theorem OAI.MatrixMultiplication.AllFieldParameters.halfMaxAxis_spec line 197
  22. theorem OAI.MatrixMultiplication.AllFieldParameters.zero_other_axis_spec line 200
  23. theorem OAI.MatrixMultiplication.AllFieldParameters.statisticWeight_le_four line 203
  24. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_outside_support line 207
  25. theorem OAI.MatrixMultiplication.AllFieldParameters.zero_nonzero_axes_distinguished line 237
  26. theorem OAI.MatrixMultiplication.AllFieldParameters.halfLaw_zero_complement line 241