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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part07
import OAI.GameTheory.SnakyConditional.Templates.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part02
import OAI.GameTheory.SnakyConditional.Templates.Level07Part05
namespace OAI
namespace SnakyConditional
def required_172 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_172 : Finset Cell := ⟨(([(-5, -1), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_172 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) required_63), (placedSet 6 (-4, 0) required_55), (placedSet 0 (-3, -1) required_64)]
def childrenD_172 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) envelope_63), (placedSet 6 (-4, 0) envelope_55), (placedSet 0 (-3, -1) envelope_64)]
theorem common_sub_172 : commonEnvelope childrenD_172 ⊆ insert (0, 0) required_172 := by decide
theorem child_required_sub_172 : ∀ j, childrenC_172 j ⊆ insert (0, 0) required_172 := by decide
theorem child_envelope_sub_172 : ∀ j, childrenD_172 j ⊆ envelope_172 := by decide
theorem pivot_mem_172 : (0, 0) ∈ envelope_172 := by decide
theorem children_work_172 : ∀ j, Template HasSnaky 5 (childrenC_172 j) (childrenD_172 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 1 (1, -1)).mono (by decide)
· exact (placed_template_map row_works_55 6 (-4, 0)).mono (by decide)
· exact (placed_template_map row_works_64 0 (-3, -1)).mono (by decide)
theorem row_works_172 : Template HasSnaky 6 required_172 envelope_172 := by
refine compose HasSnaky 5 childrenC_172 childrenD_172 children_work_172 (0, 0)
required_172 envelope_172 pivot_mem_172 child_required_sub_172 child_envelope_sub_172 ?_
intro b hb; exact common_sub_172 (mem_commonEnvelope childrenD_172 b hb)
def required_173 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_173 : Finset Cell := ⟨(([(-5, -1), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-2, 0), (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_173 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) required_63), (placedSet 6 (0, 1) required_64), (placedSet 6 (-4, 0) required_55)]
def childrenD_173 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) envelope_63), (placedSet 6 (0, 1) envelope_64), (placedSet 6 (-4, 0) envelope_55)]
theorem common_sub_173 : commonEnvelope childrenD_173 ⊆ insert (0, 0) required_173 := by decide
theorem child_required_sub_173 : ∀ j, childrenC_173 j ⊆ insert (0, 0) required_173 := by decide
theorem child_envelope_sub_173 : ∀ j, childrenD_173 j ⊆ envelope_173 := by decide
theorem pivot_mem_173 : (0, 0) ∈ envelope_173 := by decide
theorem children_work_173 : ∀ j, Template HasSnaky 5 (childrenC_173 j) (childrenD_173 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 1 (1, -1)).mono (by decide)
· exact (placed_template_map row_works_64 6 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_55 6 (-4, 0)).mono (by decide)
theorem row_works_173 : Template HasSnaky 6 required_173 envelope_173 := by
refine compose HasSnaky 5 childrenC_173 childrenD_173 children_work_173 (0, 0)
required_173 envelope_173 pivot_mem_173 child_required_sub_173 child_envelope_sub_173 ?_
intro b hb; exact common_sub_173 (mem_commonEnvelope childrenD_173 b hb)
def required_174 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_174 : Finset Cell := ⟨(([(-2, -1), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_174 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) required_58), (placedSet 1 (0, 1) required_57), (placedSet 0 (-1, 0) required_84)]
def childrenD_174 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) envelope_58), (placedSet 1 (0, 1) envelope_57), (placedSet 0 (-1, 0) envelope_84)]
theorem common_sub_174 : commonEnvelope childrenD_174 ⊆ insert (0, 0) required_174 := by decide
theorem child_required_sub_174 : ∀ j, childrenC_174 j ⊆ insert (0, 0) required_174 := by decide
theorem child_envelope_sub_174 : ∀ j, childrenD_174 j ⊆ envelope_174 := by decide
theorem pivot_mem_174 : (0, 0) ∈ envelope_174 := by decide
theorem children_work_174 : ∀ j, Template HasSnaky 5 (childrenC_174 j) (childrenD_174 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_58 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_57 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_84 0 (-1, 0)).mono (by decide)
theorem row_works_174 : Template HasSnaky 6 required_174 envelope_174 := by
refine compose HasSnaky 5 childrenC_174 childrenD_174 children_work_174 (0, 0)
required_174 envelope_174 pivot_mem_174 child_required_sub_174 child_envelope_sub_174 ?_
intro b hb; exact common_sub_174 (mem_commonEnvelope childrenD_174 b hb)
def required_175 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_175 : Finset Cell := ⟨(([(-5, 0), (-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_175 : Fin 3 → Finset Cell := ![(placedSet 0 (1, 0) required_141), (placedSet 2 (0, -1) required_7), (placedSet 1 (1, -1) required_63)]
def childrenD_175 : Fin 3 → Finset Cell := ![(placedSet 0 (1, 0) envelope_141), (placedSet 2 (0, -1) envelope_7), (placedSet 1 (1, -1) envelope_63)]
theorem common_sub_175 : commonEnvelope childrenD_175 ⊆ insert (0, 0) required_175 := by decide
theorem child_required_sub_175 : ∀ j, childrenC_175 j ⊆ insert (0, 0) required_175 := by decide
theorem child_envelope_sub_175 : ∀ j, childrenD_175 j ⊆ envelope_175 := by decide
theorem pivot_mem_175 : (0, 0) ∈ envelope_175 := by decide
theorem children_work_175 : ∀ j, Template HasSnaky 5 (childrenC_175 j) (childrenD_175 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_141 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_7 2 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_63 1 (1, -1)).mono (by decide)
theorem row_works_175 : Template HasSnaky 6 required_175 envelope_175 := by
refine compose HasSnaky 5 childrenC_175 childrenD_175 children_work_175 (0, 0)
required_175 envelope_175 pivot_mem_175 child_required_sub_175 child_envelope_sub_175 ?_
intro b hb; exact common_sub_175 (mem_commonEnvelope childrenD_175 b hb)
def required_176 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_176 : Finset Cell := ⟨(([(-5, -1), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_176 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) required_63), (placedSet 6 (0, 1) required_64), (placedSet 2 (1, 0) required_55)]
def childrenD_176 : Fin 3 → Finset Cell := ![(placedSet 1 (1, -1) envelope_63), (placedSet 6 (0, 1) envelope_64), (placedSet 2 (1, 0) envelope_55)]
theorem common_sub_176 : commonEnvelope childrenD_176 ⊆ insert (0, 0) required_176 := by decide
theorem child_required_sub_176 : ∀ j, childrenC_176 j ⊆ insert (0, 0) required_176 := by decide
theorem child_envelope_sub_176 : ∀ j, childrenD_176 j ⊆ envelope_176 := by decide
theorem pivot_mem_176 : (0, 0) ∈ envelope_176 := by decide
theorem children_work_176 : ∀ j, Template HasSnaky 5 (childrenC_176 j) (childrenD_176 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 1 (1, -1)).mono (by decide)
· exact (placed_template_map row_works_64 6 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_55 2 (1, 0)).mono (by decide)
theorem row_works_176 : Template HasSnaky 6 required_176 envelope_176 := by
refine compose HasSnaky 5 childrenC_176 childrenD_176 children_work_176 (0, 0)
required_176 envelope_176 pivot_mem_176 child_required_sub_176 child_envelope_sub_176 ?_
intro b hb; exact common_sub_176 (mem_commonEnvelope childrenD_176 b hb)
def required_177 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (-1, 0), (2, -2), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_177 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (2, -3), (2, -2), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_177 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 3 (1, 0) required_136)]
def childrenD_177 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 3 (1, 0) envelope_136)]
theorem common_sub_177 : commonEnvelope childrenD_177 ⊆ insert (0, 0) required_177 := by decide
theorem child_required_sub_177 : ∀ j, childrenC_177 j ⊆ insert (0, 0) required_177 := by decide
theorem child_envelope_sub_177 : ∀ j, childrenD_177 j ⊆ envelope_177 := by decide
theorem pivot_mem_177 : (0, 0) ∈ envelope_177 := by decide
theorem children_work_177 : ∀ j, Template HasSnaky 5 (childrenC_177 j) (childrenD_177 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_136 3 (1, 0)).mono (by decide)
theorem row_works_177 : Template HasSnaky 6 required_177 envelope_177 := by
refine compose HasSnaky 5 childrenC_177 childrenD_177 children_work_177 (0, 0)
required_177 envelope_177 pivot_mem_177 child_required_sub_177 child_envelope_sub_177 ?_
intro b hb; exact common_sub_177 (mem_commonEnvelope childrenD_177 b hb)
def required_178 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, -2), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_178 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, -3), (1, -2), (1, -1), (1, 1), (1, 2), (1, 3), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_178 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) required_37), (placedSet 1 (0, 1) required_68), (placedSet 3 (0, 1) required_46)]
def childrenD_178 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) envelope_37), (placedSet 1 (0, 1) envelope_68), (placedSet 3 (0, 1) envelope_46)]
theorem common_sub_178 : commonEnvelope childrenD_178 ⊆ insert (0, 0) required_178 := by decide
theorem child_required_sub_178 : ∀ j, childrenC_178 j ⊆ insert (0, 0) required_178 := by decide
theorem child_envelope_sub_178 : ∀ j, childrenD_178 j ⊆ envelope_178 := by decide
theorem pivot_mem_178 : (0, 0) ∈ envelope_178 := by decide
theorem children_work_178 : ∀ j, Template HasSnaky 5 (childrenC_178 j) (childrenD_178 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_37 0 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_68 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_46 3 (0, 1)).mono (by decide)
theorem row_works_178 : Template HasSnaky 6 required_178 envelope_178 := by
refine compose HasSnaky 5 childrenC_178 childrenD_178 children_work_178 (0, 0)
required_178 envelope_178 pivot_mem_178 child_required_sub_178 child_envelope_sub_178 ?_
intro b hb; exact common_sub_178 (mem_commonEnvelope childrenD_178 b hb)
end SnakyConditional
end OAI
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