OAI/Analysis/FreeEntropy/MixedGaussianSeries.lean

GitHub source file

20 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.FiniteEntropySeparation.FreeSeries.leftIndex line 10
  2. def OAI.FiniteEntropySeparation.FreeSeries.rightIndex line 11
  3. theorem OAI.FiniteEntropySeparation.FreeSeries.leftIndex_injective line 12
  4. theorem OAI.FiniteEntropySeparation.FreeSeries.rightIndex_injective line 13
  5. theorem OAI.FiniteEntropySeparation.FreeSeries.leftIndex_ne_rightIndex line 14
  6. theorem OAI.FiniteEntropySeparation.FreeSeries.joint_cases line 20
  7. def OAI.FiniteEntropySeparation.FreeSeries.gaussianJointR line 24
  8. theorem OAI.FiniteEntropySeparation.FreeSeries.gaussianJointR_nil line 26
  9. theorem OAI.FiniteEntropySeparation.FreeSeries.gaussianJointR_noise_deriv line 28
  10. theorem OAI.FiniteEntropySeparation.FreeSeries.gaussianJointR_restrict line 34
  11. theorem OAI.FiniteEntropySeparation.FreeSeries.gaussianJointR_cyclic line 40
  12. theorem OAI.FiniteEntropySeparation.FreeSeries.word_left_or_noise line 47
  13. theorem OAI.FiniteEntropySeparation.FreeSeries.mixed_gaussian_unique line 58
  14. theorem OAI.FiniteEntropySeparation.FreeSeries.moments_cumulants line 71
  15. def OAI.FiniteEntropySeparation.FreeTensor.jointTuple line 78
  16. theorem OAI.FiniteEntropySeparation.FreeTensor.jointTuple_left line 80
  17. theorem OAI.FiniteEntropySeparation.FreeTensor.jointTuple_right line 82
  18. theorem OAI.FiniteEntropySeparation.FreeTensor.jointTuple_mem line 84
  19. theorem OAI.FiniteEntropySeparation.FreeTensor.jointTuple_noise_deriv line 90
  20. theorem OAI.FiniteEntropySeparation.FreeTensor.joint_moments_cumulants line 118