OAI/Combinatorics/ContingencyTables/Dense/DenseBooleanStep.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

1. def OAI.ContingencyTables.GridBoundary.denseStepBits line 18
2. def OAI.ContingencyTables.GridBoundary.denseBitStep line 20
3. def OAI.ContingencyTables.GridBoundary.denseBitStepLaw line 29
4. theorem OAI.ContingencyTables.GridBoundary.denseBitStepLaw_eq_finite line 35
5. theorem OAI.ContingencyTables.GridBoundary.denseBitStepLaw_eq line 60

   Source documentation

   The declared q_bin+8d^5 independent unbiased bits implement exactly the transition law whose mixing bound was proved.

   theorem denseBitStepLaw_eq (R : Option I → ℕ) (P : Option J → ℕ)
       (d : ℕ) (hd : 14 ≤ d) (hR : ∀ i, d ^ 12 ≤ R i) (hP : ∀ j, d ^ 12 ≤ P j)
       (hRmax : ∀ i, R (some i) ≤ R none) (hPmax : ∀ j, P (some j) ≤ P none)
       (hdimR : Fintype.card (Option I) ≤ d) (hdimP : Fintype.card (Option J) ≤ d)
       (hfree : Fintype.card (I × J) ≤ d) (htotal : ∑ i, R i = ∑ j, P j)
       (e : I × J ≃ Fin q) (a : Grid (I := Fin q) (4 * d ^ 8)) :
   …

   Mentions: OAI.ContingencyTables.GridBoundary.Grid