OAI/Computability/UniqueGames/Foundations/Conditioning.lean

GitHub source file

16 declarations, 0 contain sorry, 0 declared as axioms

Conditioning of actual finite distributions and the selected-coordinate chain rule used in parallel repetition. A normalized conditional distribution is only constructed when the conditioning event has strictly positive probability.

  1. def OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.condition line 23
  2. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_condition line 39
  3. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_inter_eq_mul_conditional line 48
  4. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_and_le_left line 56
  5. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_and_le_right line 63
  6. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_and_eq_zero_of_probability_eq_zero line 70
  7. theorem OAI.UniqueGamesTheorem.Foundations.Games.FiniteDistribution.probability_condition_given line 77
  8. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedWins_insert line 91
  9. def OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess line 102
  10. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_nonnegative line 107
  11. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_le_one line 112
  12. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_empty line 117
  13. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_univ line 124
  14. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_antitone line 130
  15. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_insert line 136
  16. theorem OAI.UniqueGamesTheorem.Foundations.Games.Game.selectedSuccess_insert_eq_zero line 148