OAI/Combinatorics/ContingencyTables/Transport/PathAugmentation.lean

GitHub source file

14 declarations, 0 contain sorry, 0 declared as axioms

Integral augmentation along a simple path

The identities here prove conservation and capacity preservation for the literal forward-minus-reverse update in the published-input interface.

  1. def OAI.ContingencyTables.PathAugmentation.arcCount line 22
  2. def OAI.ContingencyTables.PathAugmentation.update line 25
  3. lemma OAI.ContingencyTables.PathAugmentation.arcCount_nonneg line 28
  4. lemma OAI.ContingencyTables.PathAugmentation.arcCount_eq_zero line 34
  5. lemma OAI.ContingencyTables.PathAugmentation.arcCount_eq_one line 40
  6. lemma OAI.ContingencyTables.PathAugmentation.arcCount_le_one line 51
  7. lemma OAI.ContingencyTables.PathAugmentation.row_arcCount line 59
  8. lemma OAI.ContingencyTables.PathAugmentation.column_arcCount line 69
  9. lemma OAI.ContingencyTables.PathAugmentation.path_divergence line 79
  10. lemma OAI.ContingencyTables.PathAugmentation.update_skew line 90
  11. lemma OAI.ContingencyTables.PathAugmentation.update_capacity line 98
  12. lemma OAI.ContingencyTables.PathAugmentation.update_sum line 116
  13. theorem OAI.ContingencyTables.PathAugmentation.update_feasible line 122
  14. theorem OAI.ContingencyTables.PathAugmentation.update_value line 132