OAI/Combinatorics/ContingencyTables/Counting/InitializationBrackets.lean

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11 declarations, 0 contain sorry, 0 declared as axioms

Exact local factorial sums for the companion's initial multipliers

These are the four brackets in the manuscript's exact initialization formula. The full-pair case reduces to an explicitly evaluated quadratic sum, so the rational initializer uses no factorial evaluation oracle.

  1. def OAI.ContingencyTables.InitializationBrackets.bracket line 18
  2. lemma OAI.ContingencyTables.InitializationBrackets.choose_factorial line 22
  3. lemma OAI.ContingencyTables.InitializationBrackets.shifted_choose_factorial line 26
  4. lemma OAI.ContingencyTables.InitializationBrackets.linear_sum line 35
  5. lemma OAI.ContingencyTables.InitializationBrackets.quadratic_sum line 44
  6. lemma OAI.ContingencyTables.InitializationBrackets.unshifted_sum line 67
  7. lemma OAI.ContingencyTables.InitializationBrackets.shifted_sum line 77
  8. theorem OAI.ContingencyTables.InitializationBrackets.bracket_neither line 88
  9. theorem OAI.ContingencyTables.InitializationBrackets.bracket_hole line 94
  10. theorem OAI.ContingencyTables.InitializationBrackets.bracket_full line 101
  11. theorem OAI.ContingencyTables.InitializationBrackets.bracket_both line 111