| import OAI.Combinatorics.EditApproximation.Binary.BinaryCellGrid |
| import OAI.Combinatorics.EditApproximation.Definitions |
|
|
|
|
| namespace OAI |
|
|
| /-! Literal eligibility scans for the whole-cell representative list. -/ |
|
|
| namespace EditApproximation |
| namespace BinaryFraction |
|
|
|
|
|
|
| @[simp] theorem centerEligibilityWithWork_value (b F : ℕ) (a initial : BinaryFraction) : |
| (centerEligibilityWithWork b F a initial).1 = true ↔ |
| (b : ℚ) / (4 * a.value) ≤ initial.value ∧ initial.value ≤ 8 * F * b := by |
| simp only [centerEligibilityWithWork, Bool.and_eq_true, leWithWork_value, |
| divWithWork_value, canonicalMulWithWork_value, nat_value] |
| norm_num |
|
|
| def cellCentersWithWork {n : ℕ} (P F b : ℕ) (a theta : BinaryFraction) |
| (initial : TargetInterval n → BinaryFraction) (cell : ℕ × ℕ) : |
| List (TargetInterval n) × ℕ := |
| let spacing := seedGridSpacingWithWork b P |
| let side := canonicalMulWithWork theta (nat b) |
| let states := cellStatesWithWork n (bitWordValue spacing.1) side.1 cell |
| let selected := filterWithWork (fun r => centerEligibilityWithWork b F a (initial r)) states.1 |
| (selected.1, spacing.2 + side.2 + states.2 + selected.2 + 3) |
|
|
| @[simp] theorem cellCentersWithWork_value {n : ℕ} (P F b : ℕ) (a theta : BinaryFraction) |
| (initial : TargetInterval n → BinaryFraction) (cell : ℕ × ℕ) (hP : 0 < P) : |
| (cellCentersWithWork P F b a theta initial cell).1 = |
| cellRepresentativeStates n P F b a.value (fun r => (initial r).value) theta.value cell := by |
| have htest (r : TargetInterval n) : (centerEligibilityWithWork b F a (initial r)).1 = |
| decide ((b : ℚ) / (4 * a.value) ≤ (initial r).value ∧ (initial r).value ≤ 8 * F * b) := |
| Bool.eq_iff_iff.mpr (by simp only [centerEligibilityWithWork_value, decide_eq_true_eq]) |
| simp only [cellCentersWithWork, filterWithWork_value, cellStatesWithWork_value, |
| seedGridSpacingWithWork_value b P hP, canonicalMulWithWork_value, nat_value, |
| htest, cellRepresentativeStates] |
|
|
| end BinaryFraction |
| end EditApproximation |
|
|
| end OAI |
|
|
