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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 | import OAI.GameTheory.SnakyConditional.Templates.Level05Part01
import OAI.GameTheory.SnakyConditional.Templates.Level05Part02
import OAI.GameTheory.SnakyConditional.Templates.Level05Part03
import OAI.GameTheory.SnakyConditional.Templates.Level05Part04
import OAI.GameTheory.SnakyConditional.Templates.Level05Part05
import OAI.GameTheory.SnakyConditional.Templates.Level05Part08
namespace OAI
namespace SnakyConditional
def required_124 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (-1, 0), (1, -1), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_124 : Finset Cell := ⟨(([(-2, 0), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (2, -1), (2, 0), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_124 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 2 (1, 0) required_31)]
def childrenD_124 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 2 (1, 0) envelope_31)]
theorem common_sub_124 : commonEnvelope childrenD_124 ⊆ insert (0, 0) required_124 := by decide
theorem child_required_sub_124 : ∀ j, childrenC_124 j ⊆ insert (0, 0) required_124 := by decide
theorem child_envelope_sub_124 : ∀ j, childrenD_124 j ⊆ envelope_124 := by decide
theorem pivot_mem_124 : (0, 0) ∈ envelope_124 := by decide
theorem children_work_124 : ∀ j, Template HasSnaky 3 (childrenC_124 j) (childrenD_124 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_31 2 (1, 0)).mono (by decide)
theorem row_works_124 : Template HasSnaky 4 required_124 envelope_124 := by
refine compose HasSnaky 3 childrenC_124 childrenD_124 children_work_124 (0, 0)
required_124 envelope_124 pivot_mem_124 child_required_sub_124 child_envelope_sub_124 ?_
intro b hb; exact common_sub_124 (mem_commonEnvelope childrenD_124 b hb)
def required_125 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-2, 1), (-1, -1), (-1, 1), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_125 : Finset Cell := ⟨(([(-3, -1), (-3, 1), (-2, -1), (-2, 1), (-1, -1), (-1, 1), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_125 : Fin 2 → Finset Cell := ![(placedSet 0 (0, -1) required_3), (placedSet 2 (0, 1) required_31)]
def childrenD_125 : Fin 2 → Finset Cell := ![(placedSet 0 (0, -1) envelope_3), (placedSet 2 (0, 1) envelope_31)]
theorem common_sub_125 : commonEnvelope childrenD_125 ⊆ insert (0, 0) required_125 := by decide
theorem child_required_sub_125 : ∀ j, childrenC_125 j ⊆ insert (0, 0) required_125 := by decide
theorem child_envelope_sub_125 : ∀ j, childrenD_125 j ⊆ envelope_125 := by decide
theorem pivot_mem_125 : (0, 0) ∈ envelope_125 := by decide
theorem children_work_125 : ∀ j, Template HasSnaky 3 (childrenC_125 j) (childrenD_125 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_3 0 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_31 2 (0, 1)).mono (by decide)
theorem row_works_125 : Template HasSnaky 4 required_125 envelope_125 := by
refine compose HasSnaky 3 childrenC_125 childrenD_125 children_work_125 (0, 0)
required_125 envelope_125 pivot_mem_125 child_required_sub_125 child_envelope_sub_125 ?_
intro b hb; exact common_sub_125 (mem_commonEnvelope childrenD_125 b hb)
def required_138 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 2), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_138 : Finset Cell := ⟨(([(-3, 1), (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_138 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_27), (placedSet 1 (0, 3) required_10)]
def childrenD_138 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_27), (placedSet 1 (0, 3) envelope_10)]
theorem common_sub_138 : commonEnvelope childrenD_138 ⊆ insert (0, 0) required_138 := by decide
theorem child_required_sub_138 : ∀ j, childrenC_138 j ⊆ insert (0, 0) required_138 := by decide
theorem child_envelope_sub_138 : ∀ j, childrenD_138 j ⊆ envelope_138 := by decide
theorem pivot_mem_138 : (0, 0) ∈ envelope_138 := by decide
theorem children_work_138 : ∀ j, Template HasSnaky 3 (childrenC_138 j) (childrenD_138 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_27 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_10 1 (0, 3)).mono (by decide)
theorem row_works_138 : Template HasSnaky 4 required_138 envelope_138 := by
refine compose HasSnaky 3 childrenC_138 childrenD_138 children_work_138 (0, 0)
required_138 envelope_138 pivot_mem_138 child_required_sub_138 child_envelope_sub_138 ?_
intro b hb; exact common_sub_138 (mem_commonEnvelope childrenD_138 b hb)
def required_139 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_139 : Finset Cell := ⟨(([(-3, 0), (-3, 1), (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_139 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_28), (placedSet 0 (1, 0) required_27)]
def childrenD_139 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_28), (placedSet 0 (1, 0) envelope_27)]
theorem common_sub_139 : commonEnvelope childrenD_139 ⊆ insert (0, 0) required_139 := by decide
theorem child_required_sub_139 : ∀ j, childrenC_139 j ⊆ insert (0, 0) required_139 := by decide
theorem child_envelope_sub_139 : ∀ j, childrenD_139 j ⊆ envelope_139 := by decide
theorem pivot_mem_139 : (0, 0) ∈ envelope_139 := by decide
theorem children_work_139 : ∀ j, Template HasSnaky 3 (childrenC_139 j) (childrenD_139 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_28 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_27 0 (1, 0)).mono (by decide)
theorem row_works_139 : Template HasSnaky 4 required_139 envelope_139 := by
refine compose HasSnaky 3 childrenC_139 childrenD_139 children_work_139 (0, 0)
required_139 envelope_139 pivot_mem_139 child_required_sub_139 child_envelope_sub_139 ?_
intro b hb; exact common_sub_139 (mem_commonEnvelope childrenD_139 b hb)
def required_141 : Finset Cell := ⟨(([(-5, 0), (-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_141 : Finset Cell := ⟨(([(-6, 0), (-5, 0), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_141 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) required_7), (placedSet 2 (-3, -1) required_78)]
def childrenD_141 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) envelope_7), (placedSet 2 (-3, -1) envelope_78)]
theorem common_sub_141 : commonEnvelope childrenD_141 ⊆ insert (0, 0) required_141 := by decide
theorem child_required_sub_141 : ∀ j, childrenC_141 j ⊆ insert (0, 0) required_141 := by decide
theorem child_envelope_sub_141 : ∀ j, childrenD_141 j ⊆ envelope_141 := by decide
theorem pivot_mem_141 : (0, 0) ∈ envelope_141 := by decide
theorem children_work_141 : ∀ j, Template HasSnaky 3 (childrenC_141 j) (childrenD_141 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_78 2 (-3, -1)).mono (by decide)
theorem row_works_141 : Template HasSnaky 4 required_141 envelope_141 := by
refine compose HasSnaky 3 childrenC_141 childrenD_141 children_work_141 (0, 0)
required_141 envelope_141 pivot_mem_141 child_required_sub_141 child_envelope_sub_141 ?_
intro b hb; exact common_sub_141 (mem_commonEnvelope childrenD_141 b hb)
def required_146 : Finset Cell := ⟨(([(-2, -1), (-1, -2), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_146 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_146 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) required_36), (placedSet 1 (0, 1) required_24)]
def childrenD_146 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) envelope_36), (placedSet 1 (0, 1) envelope_24)]
theorem common_sub_146 : commonEnvelope childrenD_146 ⊆ insert (0, 0) required_146 := by decide
theorem child_required_sub_146 : ∀ j, childrenC_146 j ⊆ insert (0, 0) required_146 := by decide
theorem child_envelope_sub_146 : ∀ j, childrenD_146 j ⊆ envelope_146 := by decide
theorem pivot_mem_146 : (0, 0) ∈ envelope_146 := by decide
theorem children_work_146 : ∀ j, Template HasSnaky 3 (childrenC_146 j) (childrenD_146 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_36 6 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_24 1 (0, 1)).mono (by decide)
theorem row_works_146 : Template HasSnaky 4 required_146 envelope_146 := by
refine compose HasSnaky 3 childrenC_146 childrenD_146 children_work_146 (0, 0)
required_146 envelope_146 pivot_mem_146 child_required_sub_146 child_envelope_sub_146 ?_
intro b hb; exact common_sub_146 (mem_commonEnvelope childrenD_146 b hb)
def required_149 : Finset Cell := ⟨(([(-2, 1), (-1, -3), (-1, -2), (-1, -1), (-1, 1), (0, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_149 : Finset Cell := ⟨(([(-3, 1), (-2, 1), (-1, -3), (-1, -2), (-1, -1), (-1, 1), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_149 : Fin 2 → Finset Cell := ![(placedSet 1 (0, -1) required_16), (placedSet 2 (1, 0) required_24)]
def childrenD_149 : Fin 2 → Finset Cell := ![(placedSet 1 (0, -1) envelope_16), (placedSet 2 (1, 0) envelope_24)]
theorem common_sub_149 : commonEnvelope childrenD_149 ⊆ insert (0, 0) required_149 := by decide
theorem child_required_sub_149 : ∀ j, childrenC_149 j ⊆ insert (0, 0) required_149 := by decide
theorem child_envelope_sub_149 : ∀ j, childrenD_149 j ⊆ envelope_149 := by decide
theorem pivot_mem_149 : (0, 0) ∈ envelope_149 := by decide
theorem children_work_149 : ∀ j, Template HasSnaky 3 (childrenC_149 j) (childrenD_149 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_16 1 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_24 2 (1, 0)).mono (by decide)
theorem row_works_149 : Template HasSnaky 4 required_149 envelope_149 := by
refine compose HasSnaky 3 childrenC_149 childrenD_149 children_work_149 (0, 0)
required_149 envelope_149 pivot_mem_149 child_required_sub_149 child_envelope_sub_149 ?_
intro b hb; exact common_sub_149 (mem_commonEnvelope childrenD_149 b hb)
end SnakyConditional
end OAI
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