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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 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 | import OAI.Computability.BinPacking.Inventory.PackingExclusions
import OAI.Computability.BinPacking.Trees.InventoryRowGeometry
namespace OAI
noncomputable section
namespace BinPackingGap
namespace PackingCounts
variable {D : InventoryData} {I : Instance} {b : ℕ}
def shortMainAt (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (r : D.Position) : Finset (p.TableBin (subclass e)) := by
classical
exact (Coverage.mainTuplesAt p (subclass e) (label e) v).filter fun t =>
tupleBaseline p e t = Geometry.baseline D.graph.edges.length D.R r ∧
tupleShort p e t = true
theorem main_unit_species (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (t : p.TableBin (subclass e))
(ht : t ∈ Coverage.mainTuplesAt p (subclass e) (label e) v)
(hu : D.globalUnit (globalCopy p e t) = true) :
(globalCopy p e t).1 = .up true ∨ (globalCopy p e t).1 = .um true := by
rcases hcopy : globalCopy p e t with ⟨s, i⟩
rw [hcopy] at hu
change s = .up true ∨ s = .um true
cases s with
| up one =>
change one = true at hu
exact Or.inl (congrArg GlobalSpecies.up hu)
| um one =>
change one = true at hu
exact Or.inr (congrArg GlobalSpecies.um hu)
| edge edge permit =>
have hglobal := roleCopy_subclass p e t .«global»
change D.itemSubclass ⟨.«global», globalCopy p e t⟩ = _ at hglobal
rw [hcopy] at hglobal
have hmain := ((Coverage.mem_mainTuplesAt p (subclass e) (label e) v t).mp ht).2.2
exfalso
apply hmain
cases hpattern : p.tablePattern (subclass e) t <;>
rw [hpattern] at hglobal <;> cases hglobal
theorem row_minus_of_global_um (p : Packing I b) (e : D.Item ≃ I.Item)
(t : p.TableBin (subclass e)) (hu : (globalCopy p e t).1 = .um true) :
D.rowSubclass (rowCopy p e t).2 = .tm := by
have hg := roleCopy_subclass p e t .«global»
have hx := roleCopy_subclass p e t .x
have hclass : D.itemSubclass ⟨.«global», globalCopy p e t⟩ = .um := by
rcases hcopy : globalCopy p e t with ⟨s, i⟩
have hs : s = .um true := by simpa only [hcopy] using hu
subst s
rfl
have hpat : p.tablePattern (subclass e) t = .minusTree := by
rw [hclass] at hg
cases hp : p.tablePattern (subclass e) t <;> simp_all [patternSubclass]
rw [hpat] at hx
change D.itemSubclass ⟨.x, rowCopy p e t⟩ = .tm at hx
rcases hc : rowCopy p e t with ⟨w, r⟩
rw [hc] at hx
exact hx
theorem job_covering_global_not_um (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (r : D.Position) (t : p.TableBin (subclass e))
(ht : t ∈ tupleCovering p e v
(Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L r)) :
(globalCopy p e t).1 ≠ .um true := by
intro hu
have hrow := row_minus_of_global_um p e t hu
apply D.minus_row_not_cover_jobInterior (rowCopy p e t).2 (globalCopy p e t)
(localCopy p e t).2 hrow r
exact ((mem_tupleCovering p e v _ t).mp ht).2
theorem zero_resources_job_cover (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (r : D.Position) (t : p.TableBin (subclass e))
(ht : t ∈ tupleCovering p e v
(Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L r))
(hg : tupleGlobalLength p e t = 0) (hl : tupleLocalLength p e t = 0) :
tupleBaseline p e t = Geometry.baseline D.graph.edges.length D.R r ∧
tupleShort p e t = true := by
have hmem := ((mem_tupleCovering p e v _ t).mp ht).2
have hshort : tupleShort p e t = true := by
cases hs : tupleShort p e t with
| false =>
have hfinish : tupleFinish p e t = tupleBaseline p e t := by
simp [tupleFinish, hs, hg, hl]
rw [hfinish] at hmem
exact (not_lt_of_ge hmem.1 hmem.2).elim
| true => rfl
obtain ⟨j, hj, _, hinter⟩ := D.row_zero_resources_job (rowCopy p e t).2 hshort
have hmem' : Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L r ∈
completionInterval (D.rowBaseline (rowCopy p e t).2)
(D.rowShort (rowCopy p e t).2) 0 0
(Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) := by
change completion _ _ 0 0 _ ≤ _ ∧ _ < _
simpa only [tupleFinish, hg, hl, tupleBaseline, tupleShort] using hmem
rw [hinter] at hmem'
have hpos : D.jobPosition j = r :=
(Geometry.jobInterior_mem_jobTestInterval_iff D.geometryBound D.L).mp hmem'
refine ⟨?_, hshort⟩
simp only [tupleBaseline, hj, InventoryData.rowBaseline, hpos]
theorem nonexcluded_covering_subset (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (r : D.Position) (hr : r ∉ excludedAt p e v) :
tupleCovering p e v (Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L r) ⊆
fundedTuples p e (.up true) v ∪ shortMainAt p e v r := by
classical
intro t ht
have hM := ((mem_tupleCovering p e v _ t).mp ht).1
by_cases hu : D.globalUnit (globalCopy p e t) = true
· have hspec := main_unit_species p e v t hM hu
rcases hspec with hp | hm
· exact Finset.mem_union_left _ ((mem_fundedTuples p e (.up true) v t).mpr
⟨hM, (selected_global_resource_iff p e t (.up true)).mpr hp⟩)
· exact (job_covering_global_not_um p e v r t ht hm).elim
· have hfalse : D.globalUnit (globalCopy p e t) = false := Bool.eq_false_of_not_eq_true hu
have hnot := covering_not_selected_of_nonexcluded p e v r hr t ht
have hnotpos : p.itemAtRole (subclass e) t .«local» ∉ positiveLocalResources e v := by
intro hp
exact hnot ((mem_zeroPositiveTuples p e v t).mpr ⟨hM, hfalse, hp⟩)
have hlocal := tupleLocalLength_eq_zero_of_not_positive p e v t
(Coverage.mainTuplesAt_subset_good p (subclass e) (label e) v hM) hnotpos
have hz := zero_resources_job_cover p e v r t ht
(tupleGlobalLength_eq_of_unit_false p e t hfalse) hlocal
exact Finset.mem_union_right _ (Finset.mem_filter.mpr ⟨hM, hz⟩)
theorem nonexcluded_coverage_upper (p : Packing I b) (e : D.Item ≃ I.Item)
(v : D.Vertex) (r : D.Position) (hr : r ∉ excludedAt p e v) :
(tupleCovering p e v
(Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L r)).card ≤
xplus p e v + (shortMainAt p e v r).card := by
calc
_ ≤ (fundedTuples p e (.up true) v ∪ shortMainAt p e v r).card :=
Finset.card_le_card (nonexcluded_covering_subset p e v r hr)
_ ≤ _ := Finset.card_union_le _ _
end PackingCounts
end BinPackingGap
end
end OAI
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