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720fa25 | 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 | import OAI.GameTheory.SnakyConditional.Templates.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part02
import OAI.GameTheory.SnakyConditional.Templates.Level07Part03
import OAI.GameTheory.SnakyConditional.Templates.Level07Part04
namespace OAI
namespace SnakyConditional
def required_144 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_144 : Finset Cell := ⟨(([(-6, 0), (-5, 0), (-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_144 : Fin 3 → Finset Cell := ![(placedSet 0 (0, 1) required_7), (placedSet 4 (-3, 1) required_104), (placedSet 0 (1, 0) required_55)]
def childrenD_144 : Fin 3 → Finset Cell := ![(placedSet 0 (0, 1) envelope_7), (placedSet 4 (-3, 1) envelope_104), (placedSet 0 (1, 0) envelope_55)]
theorem common_sub_144 : commonEnvelope childrenD_144 ⊆ insert (0, 0) required_144 := by decide
theorem child_required_sub_144 : ∀ j, childrenC_144 j ⊆ insert (0, 0) required_144 := by decide
theorem child_envelope_sub_144 : ∀ j, childrenD_144 j ⊆ envelope_144 := by decide
theorem pivot_mem_144 : (0, 0) ∈ envelope_144 := by decide
theorem children_work_144 : ∀ j, Template HasSnaky 5 (childrenC_144 j) (childrenD_144 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_104 4 (-3, 1)).mono (by decide)
· exact (placed_template_map row_works_55 0 (1, 0)).mono (by decide)
theorem row_works_144 : Template HasSnaky 6 required_144 envelope_144 := by
refine compose HasSnaky 5 childrenC_144 childrenD_144 children_work_144 (0, 0)
required_144 envelope_144 pivot_mem_144 child_required_sub_144 child_envelope_sub_144 ?_
intro b hb; exact common_sub_144 (mem_commonEnvelope childrenD_144 b hb)
def required_145 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, -3), (1, -2), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_145 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_145 : Fin 2 → Finset Cell := ![(placedSet 5 (0, 1) required_0), (placedSet 0 (-1, 0) required_91)]
def childrenD_145 : Fin 2 → Finset Cell := ![(placedSet 5 (0, 1) envelope_0), (placedSet 0 (-1, 0) envelope_91)]
theorem common_sub_145 : commonEnvelope childrenD_145 ⊆ insert (0, 0) required_145 := by decide
theorem child_required_sub_145 : ∀ j, childrenC_145 j ⊆ insert (0, 0) required_145 := by decide
theorem child_envelope_sub_145 : ∀ j, childrenD_145 j ⊆ envelope_145 := by decide
theorem pivot_mem_145 : (0, 0) ∈ envelope_145 := by decide
theorem children_work_145 : ∀ j, Template HasSnaky 5 (childrenC_145 j) (childrenD_145 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 5 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_91 0 (-1, 0)).mono (by decide)
theorem row_works_145 : Template HasSnaky 6 required_145 envelope_145 := by
refine compose HasSnaky 5 childrenC_145 childrenD_145 children_work_145 (0, 0)
required_145 envelope_145 pivot_mem_145 child_required_sub_145 child_envelope_sub_145 ?_
intro b hb; exact common_sub_145 (mem_commonEnvelope childrenD_145 b hb)
def required_148 : Finset Cell := ⟨(([(-1, -2), (0, -4), (0, -3), (0, -2), (0, -1), (1, -2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_148 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_148 : Fin 4 → Finset Cell := ![(placedSet 1 (1, 0) required_7), (placedSet 1 (0, 1) required_46), (placedSet 0 (1, -1) required_94), (placedSet 1 (0, 1) required_97)]
def childrenD_148 : Fin 4 → Finset Cell := ![(placedSet 1 (1, 0) envelope_7), (placedSet 1 (0, 1) envelope_46), (placedSet 0 (1, -1) envelope_94), (placedSet 1 (0, 1) envelope_97)]
theorem common_sub_148 : commonEnvelope childrenD_148 ⊆ insert (0, 0) required_148 := by decide
theorem child_required_sub_148 : ∀ j, childrenC_148 j ⊆ insert (0, 0) required_148 := by decide
theorem child_envelope_sub_148 : ∀ j, childrenD_148 j ⊆ envelope_148 := by decide
theorem pivot_mem_148 : (0, 0) ∈ envelope_148 := by decide
theorem children_work_148 : ∀ j, Template HasSnaky 5 (childrenC_148 j) (childrenD_148 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_46 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_94 0 (1, -1)).mono (by decide)
· exact (placed_template_map row_works_97 1 (0, 1)).mono (by decide)
theorem row_works_148 : Template HasSnaky 6 required_148 envelope_148 := by
refine compose HasSnaky 5 childrenC_148 childrenD_148 children_work_148 (0, 0)
required_148 envelope_148 pivot_mem_148 child_required_sub_148 child_envelope_sub_148 ?_
intro b hb; exact common_sub_148 (mem_commonEnvelope childrenD_148 b hb)
def required_150 : Finset Cell := ⟨(([(-5, 0), (-4, -1), (-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_150 : Finset Cell := ⟨(([(-5, 0), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_150 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) required_4), (placedSet 5 (-2, 1) required_126)]
def childrenD_150 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) envelope_4), (placedSet 5 (-2, 1) envelope_126)]
theorem common_sub_150 : commonEnvelope childrenD_150 ⊆ insert (0, 0) required_150 := by decide
theorem child_required_sub_150 : ∀ j, childrenC_150 j ⊆ insert (0, 0) required_150 := by decide
theorem child_envelope_sub_150 : ∀ j, childrenD_150 j ⊆ envelope_150 := by decide
theorem pivot_mem_150 : (0, 0) ∈ envelope_150 := by decide
theorem children_work_150 : ∀ j, Template HasSnaky 5 (childrenC_150 j) (childrenD_150 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 6 (-3, -1)).mono (by decide)
· exact (placed_template_map row_works_126 5 (-2, 1)).mono (by decide)
theorem row_works_150 : Template HasSnaky 6 required_150 envelope_150 := by
refine compose HasSnaky 5 childrenC_150 childrenD_150 children_work_150 (0, 0)
required_150 envelope_150 pivot_mem_150 child_required_sub_150 child_envelope_sub_150 ?_
intro b hb; exact common_sub_150 (mem_commonEnvelope childrenD_150 b hb)
def required_152 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_152 : Finset Cell := ⟨(([(0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (3, -1), (3, 0), (3, 1), (4, -1), (4, 0), (4, 1), (5, -1), (5, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_152 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 1 (3, 0) required_73)]
def childrenD_152 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 1 (3, 0) envelope_73)]
theorem common_sub_152 : commonEnvelope childrenD_152 ⊆ insert (0, 0) required_152 := by decide
theorem child_required_sub_152 : ∀ j, childrenC_152 j ⊆ insert (0, 0) required_152 := by decide
theorem child_envelope_sub_152 : ∀ j, childrenD_152 j ⊆ envelope_152 := by decide
theorem pivot_mem_152 : (0, 0) ∈ envelope_152 := by decide
theorem children_work_152 : ∀ j, Template HasSnaky 5 (childrenC_152 j) (childrenD_152 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_73 1 (3, 0)).mono (by decide)
theorem row_works_152 : Template HasSnaky 6 required_152 envelope_152 := by
refine compose HasSnaky 5 childrenC_152 childrenD_152 children_work_152 (0, 0)
required_152 envelope_152 pivot_mem_152 child_required_sub_152 child_envelope_sub_152 ?_
intro b hb; exact common_sub_152 (mem_commonEnvelope childrenD_152 b hb)
def required_154 : Finset Cell := ⟨(([(1, 0), (2, 0), (3, 0), (4, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_154 : Finset Cell := ⟨(([(-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1), (4, 0), (4, 1), (5, 0), (6, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_154 : Fin 2 → Finset Cell := ![(placedSet 6 (0, -1) required_7), (placedSet 0 (3, 1) required_104)]
def childrenD_154 : Fin 2 → Finset Cell := ![(placedSet 6 (0, -1) envelope_7), (placedSet 0 (3, 1) envelope_104)]
theorem common_sub_154 : commonEnvelope childrenD_154 ⊆ insert (0, 0) required_154 := by decide
theorem child_required_sub_154 : ∀ j, childrenC_154 j ⊆ insert (0, 0) required_154 := by decide
theorem child_envelope_sub_154 : ∀ j, childrenD_154 j ⊆ envelope_154 := by decide
theorem pivot_mem_154 : (0, 0) ∈ envelope_154 := by decide
theorem children_work_154 : ∀ j, Template HasSnaky 5 (childrenC_154 j) (childrenD_154 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 6 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_104 0 (3, 1)).mono (by decide)
theorem row_works_154 : Template HasSnaky 6 required_154 envelope_154 := by
refine compose HasSnaky 5 childrenC_154 childrenD_154 children_work_154 (0, 0)
required_154 envelope_154 pivot_mem_154 child_required_sub_154 child_envelope_sub_154 ?_
intro b hb; exact common_sub_154 (mem_commonEnvelope childrenD_154 b hb)
def required_156 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-3, 1), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_156 : Finset Cell := ⟨(([(-4, -1), (-4, 1), (-3, -1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_156 : Fin 3 → Finset Cell := ![(placedSet 0 (-2, 0) required_11), (placedSet 2 (-2, 0) required_98), (placedSet 0 (-2, -1) required_33)]
def childrenD_156 : Fin 3 → Finset Cell := ![(placedSet 0 (-2, 0) envelope_11), (placedSet 2 (-2, 0) envelope_98), (placedSet 0 (-2, -1) envelope_33)]
theorem common_sub_156 : commonEnvelope childrenD_156 ⊆ insert (0, 0) required_156 := by decide
theorem child_required_sub_156 : ∀ j, childrenC_156 j ⊆ insert (0, 0) required_156 := by decide
theorem child_envelope_sub_156 : ∀ j, childrenD_156 j ⊆ envelope_156 := by decide
theorem pivot_mem_156 : (0, 0) ∈ envelope_156 := by decide
theorem children_work_156 : ∀ j, Template HasSnaky 5 (childrenC_156 j) (childrenD_156 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_11 0 (-2, 0)).mono (by decide)
· exact (placed_template_map row_works_98 2 (-2, 0)).mono (by decide)
· exact (placed_template_map row_works_33 0 (-2, -1)).mono (by decide)
theorem row_works_156 : Template HasSnaky 6 required_156 envelope_156 := by
refine compose HasSnaky 5 childrenC_156 childrenD_156 children_work_156 (0, 0)
required_156 envelope_156 pivot_mem_156 child_required_sub_156 child_envelope_sub_156 ?_
intro b hb; exact common_sub_156 (mem_commonEnvelope childrenD_156 b hb)
end SnakyConditional
end OAI
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