OAI/InformationTheory/BooleanNoise/PerspectiveInequality.lean

GitHub source file

29 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.LeanBlast.CourtadeKumar.logBarrier line 24
  2. theorem OAI.LeanBlast.CourtadeKumar.logBarrier_zero line 26
  3. theorem OAI.LeanBlast.CourtadeKumar.hasDerivAt_logBarrier line 28
  4. theorem OAI.LeanBlast.CourtadeKumar.lambda_truncated_upper line 35
  5. theorem OAI.LeanBlast.CourtadeKumar.lambda_cutoff_four line 56
  6. theorem OAI.LeanBlast.CourtadeKumar.sq_lt_one_of_nonneg line 64
  7. theorem OAI.LeanBlast.CourtadeKumar.lambda_cutoff_two_sq line 68
  8. def OAI.LeanBlast.CourtadeKumar.lambdaDerivativeFactor line 75
  9. theorem OAI.LeanBlast.CourtadeKumar.lambda_polynomial_le_factor line 79
  10. def OAI.LeanBlast.CourtadeKumar.lambdaAuxiliary line 88
  11. def OAI.LeanBlast.CourtadeKumar.lambdaAuxiliaryDerivative line 91
  12. theorem OAI.LeanBlast.CourtadeKumar.lambdaAuxiliary_zero line 95
  13. theorem OAI.LeanBlast.CourtadeKumar.hasDerivAt_lambdaAuxiliary line 98
  14. theorem OAI.LeanBlast.CourtadeKumar.lambdaAuxiliaryDerivative_factor line 113
  15. theorem OAI.LeanBlast.CourtadeKumar.lambdaDerivativeFactor_pos line 129
  16. theorem OAI.LeanBlast.CourtadeKumar.lambdaAuxiliaryDerivative_nonneg line 136
  17. theorem OAI.LeanBlast.CourtadeKumar.monotoneOn_lambdaAuxiliary line 145
  18. theorem OAI.LeanBlast.CourtadeKumar.lambdaAuxiliary_nonneg line 155
  19. theorem OAI.LeanBlast.CourtadeKumar.lambdaAuxiliary_eq line 160
  20. theorem OAI.LeanBlast.CourtadeKumar.lambda_add_sq_le line 166
  21. theorem OAI.LeanBlast.CourtadeKumar.lambda_sqrt_add_le line 177
  22. theorem OAI.LeanBlast.CourtadeKumar.concave_perspective_exchange line 185
  23. theorem OAI.LeanBlast.CourtadeKumar.perspective_kernel_upper line 210
  24. theorem OAI.LeanBlast.CourtadeKumar.lt_weight_of_le_weight_sq line 224
  25. theorem OAI.LeanBlast.CourtadeKumar.lambda_trapezoid_bound line 231
  26. theorem OAI.LeanBlast.CourtadeKumar.perspective_inequality_of_adjusted_concave line 258
  27. theorem OAI.LeanBlast.CourtadeKumar.LSecondDeriv_curvature_bound line 280
  28. theorem OAI.LeanBlast.CourtadeKumar.concaveOn_L_logCorrectedPerspective line 287
  29. theorem OAI.LeanBlast.CourtadeKumar.perspective_inequality line 295