| import OAI.Combinatorics.ContingencyTables.Sampling.ExactMatrixTrial |
| import OAI.Combinatorics.ContingencyTables.Sampling.OriginalBoxLaw |
|
|
| namespace OAI |
|
|
| /-! |
|
|
| namespace ContingencyTables.ExactMatrixTrial |
| open ProfilePrograms DensePrograms OriginalTableBox |
| open scoped BigOperators Classical |
| noncomputable section |
|
|
| variable {m n : ℕ} (r : Fin m → ℕ) (c : Fin n → ℕ) |
|
|
| lemma lookup_index (fallback X : Table r c) : |
| lookup ((originalCandidates (List.ofFn r,List.ofFn c),matrixCode fallback.val), |
| (index r c le_rfl X).val)=matrixCode X.val := by |
| rw [lookup,candidates_code] |
| simp only [List.getD_eq_getElem?_getD,List.getElem?_ofFn,Fin.isLt,dite_true,Option.getD_some] |
| rw [OriginalBoxLaw.tableAt_index] |
| rfl |
|
|
| /-- Even a malformed index returns the fixed feasible fallback. -/ |
| lemma lookup_feasible (fallback : Table r c) (i : ℕ) : |
| ∃ X : Table r c, |
| lookup ((originalCandidates (List.ofFn r,List.ofFn c),matrixCode fallback.val),i)= |
| matrixCode X.val := by |
| rw [lookup,candidates_code] |
| by_cases hi : i<((∑ j,r j)+1)^(m*n) |
| · simp only [List.getD_eq_getElem?_getD,List.getElem?_ofFn,hi,dite_true,Option.getD_some] |
| cases hx : tableAt r c (⟨i,hi⟩ : Index m n (∑ j,r j)) with |
| | none => exact ⟨fallback,rfl⟩ |
| | some X => exact ⟨X,rfl⟩ |
| · simp only [List.getD_eq_getElem?_getD,List.getElem?_ofFn,hi,dite_false,Option.getD_none] |
| exact ⟨fallback,rfl⟩ |
|
|
| end |
| end ContingencyTables.ExactMatrixTrial |
|
|
| end OAI |
|
|
