openAI-math-dataset / lean /OAI /Combinatorics /EditApproximation /Specification /RawBandOuterBridges.lean
| import OAI.Combinatorics.EditApproximation.Specification.RawBandOuter | |
| import OAI.Combinatorics.EditApproximation.Specification.RawBandBridges | |
| import OAI.Combinatorics.EditApproximation.Definitions | |
| namespace OAI.EditApproximation.BinaryFraction | |
| theorem dyadicSampledGroupActionReadWithWorkRaw_eq {α : Type*} (source target : List α) {M : ℕ} | |
| (parent : TargetInterval source.length) (b P exponent Q : ℕ) (tau F : BinaryFraction) | |
| (child : Fin M → TargetInterval target.length → BinaryFraction) | |
| (initial current : Fin M → TargetInterval target.length → BinaryFraction × ℕ) | |
| (raw : List BinaryFraction) (hraw : raw.map value = groupDyadicScales M b F.value) | |
| (draw : ∀ t : Fin (groupDyadicScales M b F.value).length, | |
| Fin (groupSampleCount M Q b (groupDyadicScaleAt M b F.value t)) → Fin M) | |
| (members : List (UnskippedBand source target parent b P exponent tau.value F.value | |
| (fun i q => (child i q).value) (fun i q => (initial i q).1.value))) (hne : members ≠ []) : | |
| dyadicSampledGroupActionReadWithWorkRaw b exponent Q F initial current raw hraw draw | |
| (members.map UnskippedBand.raw) (by simpa using hne) = | |
| dyadicSampledGroupActionReadWithWork source target parent b P exponent Q tau F child initial current | |
| raw hraw draw members hne := by | |
| exact sampledGroupActionReadWithWorkRaw_eq source target parent b P exponent Q tau F child initial current | |
| _ _ members hne | |
| theorem preparedOnlineReadWithWorkRaw_eq : = := by | |
| funext α source target M parent P F exponent H b hb hP tau eta kappa child initial table R hc hi t center integer | |
| unfold preparedOnlineReadWithWorkRaw preparedOnlineReadWithWork | |
| rw [preparedUnskippedReadWithWorkRaw_eq source target parent b P exponent hb hP tau (nat F) | |
| child initial R R hc hi center] | |
| simp only [Prod.map, id_eq, Option.isSome_map] | |
| theorem preparedOnlineReadAllocationRaw_eq : = := by | |
| funext α source target M parent P F exponent H b hb hP tau eta kappa child initial table R hc hi | |
| childAllocation initialAllocation tableAllocation t center integer | |
| unfold preparedOnlineReadAllocationRaw preparedOnlineReadAllocation | |
| rw [preparedUnskippedReadWithWorkRaw_eq source target parent b P exponent hb hP tau (nat F) | |
| child initial R R hc hi center] | |
| simp only [Prod.map, Option.isSome_map] | |
| theorem preparedCellGroupReadWithWorkRaw_eq : = := by | |
| funext α source target M parent b P F exponent Q hb hP tau a parentInitial child initial current | |
| R C hr hi raw hraw draw cell | |
| have hreader := funext (preparedUnskippedReadWithWorkRaw_eq source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) | |
| let centers := (cellCentersReadWithWork P F b a (inversePowerTwo exponent) parentInitial cell).1 | |
| have hmembers : filterMapWithWork | |
| (preparedUnskippedReadWithWorkRaw parent b P exponent tau (nat F) child initial) centers = | |
| Prod.map (List.map UnskippedBand.raw) id (filterMapWithWork | |
| (preparedUnskippedReadWithWork source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) centers) := by | |
| rw [hreader] | |
| exact filterMapWithWork_map_raw _ _ _ | |
| dsimp only [centers] at hmembers | |
| unfold preparedCellGroupReadWithWorkRaw preparedCellGroupReadWithWork | |
| simp only [hmembers] | |
| simp only [Prod.map, id_eq, List.map_eq_nil_iff] | |
| split_ifs with h | |
| · rfl | |
| · rw [dyadicSampledGroupActionReadWithWorkRaw_eq] | |
| theorem preparedCellGroupSourceWithWorkRaw_eq : = := by | |
| funext α source target M parent b P F exponent Q hb hP tau a parentInitial child initial current | |
| R C hr hi raw hraw draw cell | |
| have hreader := funext (preparedUnskippedReadWithWorkRaw_eq source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) | |
| let centers := (cellCentersReadWithWork P F b a (inversePowerTwo exponent) parentInitial cell).1 | |
| have hmembers : filterMapWithWork | |
| (preparedUnskippedReadWithWorkRaw parent b P exponent tau (nat F) child initial) centers = | |
| Prod.map (List.map UnskippedBand.raw) id (filterMapWithWork | |
| (preparedUnskippedReadWithWork source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) centers) := by | |
| rw [hreader] | |
| exact filterMapWithWork_map_raw _ _ _ | |
| dsimp only [centers] at hmembers | |
| unfold preparedCellGroupSourceWithWorkRaw preparedCellGroupSourceWithWork | |
| simp only [hmembers] | |
| simp only [Prod.map, id_eq, List.map_eq_nil_iff] | |
| split_ifs with h | |
| · rfl | |
| · rw [sampledGroupActionSourceWithWorkRaw_eq] | |
| theorem preparedCellGroupSourceAllocationRaw_eq : = := by | |
| funext α source target M parent b P F exponent Q hb hP tau a parentInitial child initial current | |
| R C hr hi raw hraw draw parentAllocation childAllocation initialAllocation currentAllocation drawAllocation cell | |
| have hreader := funext (preparedUnskippedReadWithWorkRaw_eq source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) | |
| let centers := (cellCentersReadWithWork P F b a (inversePowerTwo exponent) parentInitial cell).1 | |
| have hmembers : filterMapWithWork | |
| (preparedUnskippedReadWithWorkRaw parent b P exponent tau (nat F) child initial) centers = | |
| Prod.map (List.map UnskippedBand.raw) id (filterMapWithWork | |
| (preparedUnskippedReadWithWork source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) centers) := by | |
| rw [hreader] | |
| exact filterMapWithWork_map_raw _ _ _ | |
| have hallocation : filterMapAllocation | |
| (preparedUnskippedReadWithWorkRaw parent b P exponent tau (nat F) child initial) | |
| (fun center => preparedUnskippedReadAllocation parent center b P exponent tau (nat F) | |
| child initial childAllocation initialAllocation) centers = | |
| filterMapAllocation | |
| (preparedUnskippedReadWithWork source target parent b P exponent hb hP tau (nat F) | |
| child initial R C hr hi) | |
| (fun center => preparedUnskippedReadAllocation parent center b P exponent tau (nat F) | |
| child initial childAllocation initialAllocation) centers := by | |
| rw [hreader] | |
| exact filterMapAllocation_map_raw _ _ _ _ | |
| dsimp only [centers] at hmembers hallocation | |
| unfold preparedCellGroupSourceAllocationRaw preparedCellGroupSourceAllocation | |
| simp only [hmembers, hallocation] | |
| simp only [Prod.map, id_eq, List.map_eq_nil_iff] | |
| split_ifs with h | |
| · rfl | |
| · rw [sampledGroupActionSourceAllocationRaw_eq] | |
| end OAI.EditApproximation.BinaryFraction | |