OAI/InformationTheory/PhotonNumber/Duality.lean

GitHub source file

32 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.EntropyPhotonNumber.SpectralLogData.ambientDefect_normalize line 11
  2. theorem OAI.TensorLp.conditionalLeft_eq_of_operator line 43
  3. theorem OAI.TensorLp.conditionalRight_eq_of_operator line 58
  4. theorem OAI.EntropyPhotonNumber.joint_dual_conjugate line 78
  5. theorem OAI.EntropyPhotonNumber.first_dual_conditional line 90
  6. theorem OAI.EntropyPhotonNumber.WeightedColumns.rawSlice_root line 109
  7. theorem OAI.EntropyPhotonNumber.WeightedColumns.rawSliceRight_root line 115
  8. theorem OAI.EntropyPhotonNumber.WeightedColumns.rawSlice_dual line 121
  9. theorem OAI.EntropyPhotonNumber.WeightedColumns.rawFirstSlice_physical line 126
  10. theorem OAI.EntropyPhotonNumber.WeightedColumns.rawSecondSlice_physical line 133
  11. def OAI.ThermalSpectral.scalarTarget line 147
  12. def OAI.ThermalSpectral.scalarDiagram line 153
  13. def OAI.ThermalSpectral.scalarWeight line 160
  14. theorem OAI.ThermalSpectral.scalar_comparison line 164
  15. theorem OAI.ThermalSpectral.scalar_logMean_bound line 184
  16. theorem OAI.ThermalSpectral.scalar_arithmetic_BKM line 208
  17. def OAI.EnsembleL2.meanLM line 245
  18. def OAI.EnsembleL2.mixtureFunctional line 254
  19. theorem OAI.EnsembleL2.mixtureFunctional_apply line 260
  20. theorem OAI.EnsembleL2.mixtureFunctional_square line 266
  21. theorem OAI.EnsembleL2.mixtureFunctional_adjoint_square line 273
  22. theorem OAI.ThermalSpectral.mixture_arithmetic_bounds line 287
  23. theorem OAI.ThermalSpectral.mixture_BKM_bound line 320
  24. theorem OAI.ThermalDual.weighted_sum_bound line 335
  25. theorem OAI.ThermalDual.weighted_functionals_bound line 343
  26. theorem OAI.ThermalDual.modes_triangle line 357
  27. theorem OAI.ThermalDual.defect_young line 374
  28. theorem OAI.ThermalSpectral.mixture_thermal_bound line 400
  29. theorem OAI.ThermalDual.dual_bound_from_core line 421
  30. theorem OAI.ThermalDual.two_sqrt_norm_sq line 462
  31. theorem OAI.ThermalDual.aggregate_bound line 471
  32. theorem OAI.ThermalDual.real_mul_inverse_sqrt line 515