| import OAI.Computability.BinPacking.Inventory.PackingConstantPool | |
| namespace OAI | |
| noncomputable section | |
| namespace BinPackingGap.GraphPackingStockStreams | |
| open PackingConstantPool PackingInventoryDescriptors PackingDescriptorExpression | |
| theorem repeatRecords_rawRecord (pair : Nat × Nat) (n : Nat) : | |
| repeatRecords (rawRecord pair) n = rawRecords (List.replicate n pair) := by | |
| induction n with | |
| | zero => rfl | |
| | succ n ih => | |
| simpa only [repeatRecords, List.replicate_succ, rawRecords, List.flatMap_cons] using | |
| congrArg (fun word => rawRecord pair ++ word) ih | |
| theorem singleton_chunk_records (D : InventoryData) (label : Option D.Vertex) | |
| (edge rep : Nat) (descriptor : ItemDescriptor D) : | |
| PackingChunkMachine.records (numerator D) PackingItemExpression.denominator | |
| (fun _ => values D label edge rep) [descriptor] = | |
| rawRecord (rawOfDescriptor D label edge rep descriptor) := by | |
| simp only [PackingChunkMachine.records_cons, PackingChunkMachine.records_nil, | |
| List.append_nil, record_eq] | |
| theorem globalPoolStream_eq_replicate (D : InventoryData) (species : GlobalSpecies D.graph) : | |
| globalPoolStream D species = | |
| List.replicate (D.globalStock species) | |
| (rawOfDescriptor D none (globalEdgeIndex D species) 0 (globalDescriptor D species)) := by | |
| simp only [globalPoolStream, List.map_const', List.length_finRange] | |
| theorem flagPoolStream_eq_replicate (D : InventoryData) (species : FlagSpecies) : | |
| flagPoolStream D species = | |
| List.replicate (D.flagStock species) | |
| (rawOfDescriptor D none 0 0 (flagDescriptor D species)) := by | |
| simp only [flagPoolStream, List.map_const', List.length_finRange] | |
| theorem globalPool_records (D : InventoryData) (species : GlobalSpecies D.graph) : | |
| repeatRecords | |
| (PackingItemBlockMachine.record (numerator D (globalDescriptor D species)) | |
| PackingItemExpression.denominator (values D none (globalEdgeIndex D species) 0)) | |
| (D.globalStock species) = rawRecords (globalPoolStream D species) := by | |
| rw [record_eq, globalPoolStream_eq_replicate, repeatRecords_rawRecord] | |
| theorem flagPool_records (D : InventoryData) (species : FlagSpecies) : | |
| repeatRecords | |
| (PackingItemBlockMachine.record (numerator D (flagDescriptor D species)) | |
| PackingItemExpression.denominator (values D none 0 0)) | |
| (D.flagStock species) = rawRecords (flagPoolStream D species) := by | |
| rw [record_eq, flagPoolStream_eq_replicate, repeatRecords_rawRecord] | |
| theorem globalPool_chunk_records (D : InventoryData) (species : GlobalSpecies D.graph) : | |
| repeatRecords | |
| (PackingChunkMachine.records (numerator D) PackingItemExpression.denominator | |
| (fun _ => values D none (globalEdgeIndex D species) 0) [globalDescriptor D species]) | |
| (D.globalStock species) = rawRecords (globalPoolStream D species) := by | |
| rw [singleton_chunk_records, globalPoolStream_eq_replicate, repeatRecords_rawRecord] | |
| theorem flagPool_chunk_records (D : InventoryData) (species : FlagSpecies) : | |
| repeatRecords | |
| (PackingChunkMachine.records (numerator D) PackingItemExpression.denominator | |
| (fun _ => values D none 0 0) [flagDescriptor D species]) | |
| (D.flagStock species) = rawRecords (flagPoolStream D species) := by | |
| rw [singleton_chunk_records, flagPoolStream_eq_replicate, repeatRecords_rawRecord] | |
| end BinPackingGap.GraphPackingStockStreams | |
| end | |
| end OAI | |