File size: 3,377 Bytes
8df23f4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 | 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
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