OAI/LinearAlgebra/MatrixMultiplication/Entropy/ConditionalLabels.lean

GitHub source file

26 declarations, 0 contain sorry, 0 declared as axioms

Finite entropy, rate estimates and ordered asymptotic limits.

  1. inductive OAI.MatrixMultiplication.ReaderPair line 15
  2. abbrev OAI.MatrixMultiplication.ReaderPair.enumList line 19
  3. theorem OAI.MatrixMultiplication.ReaderPair.enumList_getElem?_ctorIdx_eq line 21
  4. theorem OAI.MatrixMultiplication.ReaderPair.enumList_nodup line 25
  5. instance OAI.MatrixMultiplication.(instance at line 30) line 30
  6. def OAI.MatrixMultiplication.ConditionalLabels.pairingSize line 45
  7. def OAI.MatrixMultiplication.ConditionalLabels.pairingRate line 49
  8. theorem OAI.MatrixMultiplication.ConditionalLabels.pairingSize_pos line 53
  9. theorem OAI.MatrixMultiplication.ConditionalLabels.pairingRate_nonneg line 62
  10. theorem OAI.MatrixMultiplication.ConditionalLabels.pairingSize_product line 71
  11. theorem OAI.MatrixMultiplication.ConditionalLabels.pairingRate_sum line 79
  12. theorem OAI.MatrixMultiplication.ConditionalLabels.tendsto_log_pairingSize line 87
  13. def OAI.MatrixMultiplication.ConditionalLabels.stagePairingSize line 114
  14. def OAI.MatrixMultiplication.ConditionalLabels.stagePairingRate line 118
  15. theorem OAI.MatrixMultiplication.ConditionalLabels.stagePairingSize_product line 122
  16. theorem OAI.MatrixMultiplication.ConditionalLabels.stagePairingRate_sum line 132
  17. theorem OAI.MatrixMultiplication.ConditionalLabels.tendsto_log_stagePairingSize line 141
  18. theorem OAI.MatrixMultiplication.ConditionalLabels.tendsto_log_stagePairingSize_normalized line 149
  19. theorem OAI.MatrixMultiplication.ConditionalLabels.auxiliary_overhead_tendsto_zero line 159
  20. theorem OAI.MatrixMultiplication.ConditionalLabels.auxiliary_overhead_nonneg line 170
  21. theorem OAI.MatrixMultiplication.ConditionalLabels.charged_cost_tendsto line 182
  22. theorem OAI.MatrixMultiplication.ConditionalLabels.limit_le_source_cost line 192
  23. def OAI.MatrixMultiplication.ConditionalLabels.lawPairingRate line 204
  24. theorem OAI.MatrixMultiplication.ConditionalLabels.lawPairingRate_sum line 209
  25. theorem OAI.MatrixMultiplication.ConditionalLabels.incident_rate_eq_prefix_entropy line 219
  26. theorem OAI.MatrixMultiplication.ConditionalLabels.remaining_rate_eq_entropy_sub_prefix line 266