| import OAI.Combinatorics.EditApproximation.Coarse.CoarseArraySimulation |
| import OAI.Combinatorics.EditApproximation.Definitions |
|
|
|
|
| namespace OAI |
|
|
| namespace EditApproximation |
| namespace BinaryFraction |
|
|
| /-- Read one array cell; absent arrays represent exact zero. -/ |
|
|
|
|
| theorem coarseBinaryRead_value (array : CoarseBinaryArray) (i : ℕ) : |
| (coarseBinaryRead array i).value = ((coarseBinaryContents array).getD [])[i]?.getD 0 := by |
| cases array with |
| | none => simp only [coarseBinaryRead, nat_value, Nat.cast_zero, coarseBinaryContents, |
| Option.map_none, Option.getD_none, List.getElem?_nil] |
| | some cells => |
| simp only [coarseBinaryRead, coarseBinaryContents, Option.map_some, Option.getD_some, |
| List.getElem?_map] |
| cases cells[i]? <;> simp only [ Option.getD_none, Option.map_none, nat_value, |
| Nat.cast_zero, Option.getD_some, Option.map_some] |
|
|
| theorem coarseBinaryRead_rep {n : ℕ} (array : CoarseBinaryArray) (spec : CoarseStoredArray n) |
| (h : CoarseArrayRep array spec) (i : Fin n) : |
| (coarseBinaryRead array i.val).value = coarseStoredRead spec i := by |
| rw [coarseBinaryRead_value, h] |
| cases spec with |
| | none => rfl |
| | some cells => |
| have hi : i.val < cells.1.length := by rw [cells.2]; exact i.isLt |
| simp only [coarseRationalContents, Option.map_some, Option.getD_some, List.getElem?_eq_getElem hi, |
| Option.getD_some, coarseStoredRead] |
|
|
| end BinaryFraction |
| end EditApproximation |
|
|
| end OAI |
|
|
