OAI/Probability/SKGap/Entropy/EntropyEll.lean

GitHub source file

28 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.SKGap.entropyEll line 14
  2. def OAI.SKGap.entropySlack line 16
  3. theorem OAI.SKGap.entropyEll_hasDerivAt line 18
  4. theorem OAI.SKGap.entropyEll_nonneg line 27
  5. theorem OAI.SKGap.entropyEll_le_half_sq_of_nonpos line 32
  6. theorem OAI.SKGap.entropySlack_pos_of_neg line 54
  7. theorem OAI.SKGap.value_le_of_deriv_nonneg line 61
  8. theorem OAI.SKGap.half_sq_le_entropyEll line 75
  9. theorem OAI.SKGap.entropySlack_cubic_lower line 87
  10. theorem OAI.SKGap.entropySlack_cubic_lower_of_le line 101
  11. theorem OAI.SKGap.entropySlack_pos line 108
  12. theorem OAI.SKGap.log_one_add_cubic_upper line 115
  13. def OAI.SKGap.entropyVarianceSlack line 129
  14. def OAI.SKGap.entropyVarianceSlope line 132
  15. theorem OAI.SKGap.entropyVarianceSlack_hasDerivAt line 135
  16. theorem OAI.SKGap.entropyVarianceSlope_hasDerivAt line 144
  17. theorem OAI.SKGap.entropyVariance_curvature_one line 153
  18. theorem OAI.SKGap.entropyVariance_taylor_lower line 161
  19. theorem OAI.SKGap.entropyVariance_at_base line 187
  20. theorem OAI.SKGap.entropyVariance_at_base_lower line 196
  21. theorem OAI.SKGap.entropyVarianceSlope_at_base line 212
  22. theorem OAI.SKGap.entropyVarianceSlope_at_base_lower line 218
  23. theorem OAI.SKGap.entropyVariance_pos_large line 234
  24. theorem OAI.SKGap.entropy_transport_complete_square line 265
  25. theorem OAI.SKGap.entropy_scalar_optimization line 273
  26. theorem OAI.SKGap.entropy_variance_function_mono line 324
  27. theorem OAI.SKGap.entropy_variance_scale line 336
  28. theorem OAI.SKGap.entropy_variance_scaled_lower line 347