OAI/InformationTheory/BooleanNoise/CubeSplits.lean

GitHub source file

33 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.LeanBlast.CourtadeKumar.cubeSplitEquiv line 16
  2. theorem OAI.LeanBlast.CourtadeKumar.sum_cube_split line 24
  3. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_split line 29
  4. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_div line 36
  5. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_half_sum line 42
  6. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_split_pair line 46
  7. theorem OAI.LeanBlast.CourtadeKumar.pairMean_add_halfDifference line 50
  8. theorem OAI.LeanBlast.CourtadeKumar.pairMean_sub_halfDifference line 55
  9. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_pairMean line 60
  10. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_pairHalfDifference line 64
  11. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_pairMean_add_halfDifference line 70
  12. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_pairMean_sub_halfDifference line 76
  13. theorem OAI.LeanBlast.CourtadeKumar.entropyAverage_split line 82
  14. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_pairEntropyGap line 86
  15. theorem OAI.LeanBlast.CourtadeKumar.informationDeficit_split line 95
  16. theorem OAI.LeanBlast.CourtadeKumar.informationDeficit_eq_pairMean_add line 105
  17. theorem OAI.LeanBlast.CourtadeKumar.meanVariance_split line 112
  18. theorem OAI.LeanBlast.CourtadeKumar.flip_zero_cases line 119
  19. theorem OAI.LeanBlast.CourtadeKumar.flip_succ_cases line 126
  20. theorem OAI.LeanBlast.CourtadeKumar.restrict_cubeDerivative_succ line 137
  21. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_first_coordinate_energy line 142
  22. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_succ_coordinate_energy line 153
  23. theorem OAI.LeanBlast.CourtadeKumar.dissipation_split line 164
  24. theorem OAI.LeanBlast.CourtadeKumar.IsInterior.restrict line 173
  25. theorem OAI.LeanBlast.CourtadeKumar.IsInterior.pairMean line 178
  26. theorem OAI.LeanBlast.CourtadeKumar.IsInterior.pairDomain line 186
  27. def OAI.LeanBlast.CourtadeKumar.cubeVariance line 204
  28. theorem OAI.LeanBlast.CourtadeKumar.cubeVariance_nonneg line 207
  29. theorem OAI.LeanBlast.CourtadeKumar.cubeVariance_eq line 210
  30. theorem OAI.LeanBlast.CourtadeKumar.average_one_sub_sq_eq_meanVariance_sub_variance line 220
  31. theorem OAI.LeanBlast.CourtadeKumar.cubeAverage_dim_zero line 226
  32. theorem OAI.LeanBlast.CourtadeKumar.informationDeficit_dim_zero line 234
  33. theorem OAI.LeanBlast.CourtadeKumar.dissipation_dim_zero line 238