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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 | import OAI.Computability.BinPacking.Packing.PackingCoordinates
namespace OAI
namespace BinPackingGap.InventoryData
variable (D : InventoryData)
private theorem node_right_in_root {T : UniformTree} (v : T.Node)
(s : TreeGeometry.Side) (hT : T.branchBound ≤ D.geometryBound) :
TreeGeometry.rootOffset s ≤
TreeGeometry.right D.graph.edges.length D.R D.geometryBound s v.val ∧
TreeGeometry.right D.graph.edges.length D.R D.geometryBound s v.val ≤
TreeGeometry.rootOffset s + 1 := by
apply TreeGeometry.nodeCell_subset_root D.graph.edges.length D.R D.geometryBound s hT v
exact ⟨(TreeGeometry.left_lt_right _ _ _ _ _).le, le_rfl⟩
theorem rowBaseline_le_one_of_not_tm {v : D.Vertex} (r : D.RowAt v)
(hclass : D.rowSubclass r ≠ .tm) : D.rowBaseline r ≤ 1 := by
rcases r with t | ⟨short, j⟩
· rcases t with ⟨node, i⟩ | ⟨node, i⟩ | i
· have h := D.node_right_in_root node .plus D.plus_branch_le_geometryBound
simpa only [rowBaseline, treeBaseline, TreeGeometry.rootOffset, zero_add] using h.2
· exact (hclass rfl).elim
· exact le_rfl
· exact (Geometry.job_baseline_lt_one _ _ _).le
theorem rowBaseline_ge_four_of_tm {v : D.Vertex} (r : D.RowAt v)
(hclass : D.rowSubclass r = .tm) : 4 ≤ D.rowBaseline r := by
rcases r with t | ⟨short, j⟩
· rcases t with ⟨node, i⟩ | ⟨node, i⟩ | i
· cases hclass
· exact (D.node_right_in_root node .minus D.minus_branch_le_geometryBound).1
· cases hclass
· cases hclass
theorem rowShort_eq_false_of_tm {v : D.Vertex} (r : D.RowAt v)
(hclass : D.rowSubclass r = .tm) : D.rowShort r = false := by
rcases r with t | ⟨short, j⟩
· rfl
· cases hclass
theorem exists_jobCopy_of_rowShort {v : D.Vertex} (r : D.RowAt v)
(hshort : D.rowShort r = true) : ∃ j : D.JobCopy v, r = .inr (true, j) := by
rcases r with t | ⟨short, j⟩
· cases hshort
· change short = true at hshort
subst short
exact ⟨j, rfl⟩
theorem row_zero_resources_empty {v : D.Vertex} (r : D.RowAt v)
(hshort : D.rowShort r = false) :
completionInterval (D.rowBaseline r) (D.rowShort r) 0 0
(Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) = ∅ := by
rw [hshort]
exact completionInterval_long_zero_lengths _ _
theorem row_zero_resources_job {v : D.Vertex} (r : D.RowAt v)
(hshort : D.rowShort r = true) :
∃ j : D.JobCopy v, r = .inr (true, j) ∧
D.rowPosition r = some (D.jobPosition j) ∧
completionInterval (D.rowBaseline r) (D.rowShort r) 0 0
(Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) =
Geometry.jobTestInterval D.graph.edges.length D.R D.geometryBound D.L
(D.jobPosition j) := by
obtain ⟨j, rfl⟩ := D.exists_jobCopy_of_rowShort r hshort
refine ⟨j, rfl, rfl, ?_⟩
exact completion_job_interval _ _ _ _ _
theorem minus_row_completion_gt_one {v w : D.Vertex} (r : D.RowAt v)
(u : D.GlobalCopy) (l : D.LocalAt w) (hclass : D.rowSubclass r = .tm) :
1 < completion (D.rowBaseline r) (D.rowShort r) (D.globalLength u)
(D.localLength l) (Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) := by
apply completion_minus_geometry_gt_one
D.graph.edges.length D.R D.geometryBound D.L
· exact D.rowBaseline_ge_four_of_tm r hclass
· exact D.rowShort_eq_false_of_tm r hclass
· exact D.globalLength_le_one u
· exact D.localLength_le_lambda_one l
theorem minus_row_not_cover_jobInterior {v w : D.Vertex} (r : D.RowAt v)
(u : D.GlobalCopy) (l : D.LocalAt w) (hclass : D.rowSubclass r = .tm)
(job : D.Position) :
Geometry.jobInterior D.graph.edges.length D.R D.geometryBound D.L job ∉
completionInterval (D.rowBaseline r) (D.rowShort r) (D.globalLength u)
(D.localLength l) (Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) := by
intro hmem
have hh := D.minus_row_completion_gt_one r u l hclass
have hj := (Geometry.closedJobCell_bounds
(Geometry.jobInterior_mem_closedJobCell D.graph.edges.length D.R
D.geometryBound D.L job)).2
exact (not_le_of_gt (hj.trans hh)) hmem.1
theorem plus_row_not_cover_minus_side {v w : D.Vertex} (r : D.RowAt v)
(u : D.GlobalCopy) (l : D.LocalAt w) (hclass : D.rowSubclass r ≠ .tm)
{a : ℚ} (ha : 4 ≤ a) :
a ∉ completionInterval (D.rowBaseline r) (D.rowShort r) (D.globalLength u)
(D.localLength l) (Geometry.delta D.graph.edges.length D.R D.geometryBound D.L) := by
apply not_mem_plus_completionInterval
· exact D.rowBaseline_le_one_of_not_tm r hclass
· linarith
end BinPackingGap.InventoryData
end OAI
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