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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 | import OAI.GameTheory.SnakyConditional.Templates.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part02
import OAI.GameTheory.SnakyConditional.Templates.Level07Part04
import OAI.GameTheory.SnakyConditional.Templates.Level07Part06
namespace OAI
namespace SnakyConditional
def required_159 : Finset Cell := ⟨(([(-1, -2), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_159 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (1, 3)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_159 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) required_45), (placedSet 1 (0, 1) required_65), (placedSet 3 (-1, 0) required_7)]
def childrenD_159 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) envelope_45), (placedSet 1 (0, 1) envelope_65), (placedSet 3 (-1, 0) envelope_7)]
theorem common_sub_159 : commonEnvelope childrenD_159 ⊆ insert (0, 0) required_159 := by decide
theorem child_required_sub_159 : ∀ j, childrenC_159 j ⊆ insert (0, 0) required_159 := by decide
theorem child_envelope_sub_159 : ∀ j, childrenD_159 j ⊆ envelope_159 := by decide
theorem pivot_mem_159 : (0, 0) ∈ envelope_159 := by decide
theorem children_work_159 : ∀ j, Template HasSnaky 5 (childrenC_159 j) (childrenD_159 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_45 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_65 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_7 3 (-1, 0)).mono (by decide)
theorem row_works_159 : Template HasSnaky 6 required_159 envelope_159 := by
refine compose HasSnaky 5 childrenC_159 childrenD_159 children_work_159 (0, 0)
required_159 envelope_159 pivot_mem_159 child_required_sub_159 child_envelope_sub_159 ?_
intro b hb; exact common_sub_159 (mem_commonEnvelope childrenD_159 b hb)
def required_160 : Finset Cell := ⟨(([(1, 0), (1, 1), (1, 2), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_160 : Finset Cell := ⟨(([(-1, -1), (0, -1), (0, 0), (1, 0), (1, 1), (1, 2), (1, 3), (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_160 : Fin 2 → Finset Cell := ![(placedSet 1 (4, -1) required_63), (placedSet 3 (0, -1) required_32)]
def childrenD_160 : Fin 2 → Finset Cell := ![(placedSet 1 (4, -1) envelope_63), (placedSet 3 (0, -1) envelope_32)]
theorem common_sub_160 : commonEnvelope childrenD_160 ⊆ insert (0, 0) required_160 := by decide
theorem child_required_sub_160 : ∀ j, childrenC_160 j ⊆ insert (0, 0) required_160 := by decide
theorem child_envelope_sub_160 : ∀ j, childrenD_160 j ⊆ envelope_160 := by decide
theorem pivot_mem_160 : (0, 0) ∈ envelope_160 := by decide
theorem children_work_160 : ∀ j, Template HasSnaky 5 (childrenC_160 j) (childrenD_160 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 1 (4, -1)).mono (by decide)
· exact (placed_template_map row_works_32 3 (0, -1)).mono (by decide)
theorem row_works_160 : Template HasSnaky 6 required_160 envelope_160 := by
refine compose HasSnaky 5 childrenC_160 childrenD_160 children_work_160 (0, 0)
required_160 envelope_160 pivot_mem_160 child_required_sub_160 child_envelope_sub_160 ?_
intro b hb; exact common_sub_160 (mem_commonEnvelope childrenD_160 b hb)
def required_161 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -2), (-1, -1), (-1, 0), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_161 : Finset Cell := ⟨(([(-3, 1), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-2, 3), (-1, -2), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_161 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_15), (placedSet 0 (1, 0) required_86)]
def childrenD_161 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_15), (placedSet 0 (1, 0) envelope_86)]
theorem common_sub_161 : commonEnvelope childrenD_161 ⊆ insert (0, 0) required_161 := by decide
theorem child_required_sub_161 : ∀ j, childrenC_161 j ⊆ insert (0, 0) required_161 := by decide
theorem child_envelope_sub_161 : ∀ j, childrenD_161 j ⊆ envelope_161 := by decide
theorem pivot_mem_161 : (0, 0) ∈ envelope_161 := by decide
theorem children_work_161 : ∀ j, Template HasSnaky 5 (childrenC_161 j) (childrenD_161 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_15 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_86 0 (1, 0)).mono (by decide)
theorem row_works_161 : Template HasSnaky 6 required_161 envelope_161 := by
refine compose HasSnaky 5 childrenC_161 childrenD_161 children_work_161 (0, 0)
required_161 envelope_161 pivot_mem_161 child_required_sub_161 child_envelope_sub_161 ?_
intro b hb; exact common_sub_161 (mem_commonEnvelope childrenD_161 b hb)
def required_162 : Finset Cell := ⟨(([(-1, -2), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_162 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_162 : Fin 4 → Finset Cell := ![(placedSet 3 (-1, 0) required_7), (placedSet 1 (0, 1) required_127), (placedSet 0 (-1, 1) required_63), (placedSet 0 (-1, -1) required_157)]
def childrenD_162 : Fin 4 → Finset Cell := ![(placedSet 3 (-1, 0) envelope_7), (placedSet 1 (0, 1) envelope_127), (placedSet 0 (-1, 1) envelope_63), (placedSet 0 (-1, -1) envelope_157)]
theorem common_sub_162 : commonEnvelope childrenD_162 ⊆ insert (0, 0) required_162 := by decide
theorem child_required_sub_162 : ∀ j, childrenC_162 j ⊆ insert (0, 0) required_162 := by decide
theorem child_envelope_sub_162 : ∀ j, childrenD_162 j ⊆ envelope_162 := by decide
theorem pivot_mem_162 : (0, 0) ∈ envelope_162 := by decide
theorem children_work_162 : ∀ j, Template HasSnaky 5 (childrenC_162 j) (childrenD_162 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 3 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_127 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_63 0 (-1, 1)).mono (by decide)
· exact (placed_template_map row_works_157 0 (-1, -1)).mono (by decide)
theorem row_works_162 : Template HasSnaky 6 required_162 envelope_162 := by
refine compose HasSnaky 5 childrenC_162 childrenD_162 children_work_162 (0, 0)
required_162 envelope_162 pivot_mem_162 child_required_sub_162 child_envelope_sub_162 ?_
intro b hb; exact common_sub_162 (mem_commonEnvelope childrenD_162 b hb)
def required_169 : Finset Cell := ⟨(([(0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_169 : Finset Cell := ⟨(([(-1, 1), (0, 0), (0, 1), (0, 2), (0, 3), (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_169 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_28), (placedSet 1 (4, -1) required_63)]
def childrenD_169 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_28), (placedSet 1 (4, -1) envelope_63)]
theorem common_sub_169 : commonEnvelope childrenD_169 ⊆ insert (0, 0) required_169 := by decide
theorem child_required_sub_169 : ∀ j, childrenC_169 j ⊆ insert (0, 0) required_169 := by decide
theorem child_envelope_sub_169 : ∀ j, childrenD_169 j ⊆ envelope_169 := by decide
theorem pivot_mem_169 : (0, 0) ∈ envelope_169 := by decide
theorem children_work_169 : ∀ j, Template HasSnaky 5 (childrenC_169 j) (childrenD_169 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_28 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_63 1 (4, -1)).mono (by decide)
theorem row_works_169 : Template HasSnaky 6 required_169 envelope_169 := by
refine compose HasSnaky 5 childrenC_169 childrenD_169 children_work_169 (0, 0)
required_169 envelope_169 pivot_mem_169 child_required_sub_169 child_envelope_sub_169 ?_
intro b hb; exact common_sub_169 (mem_commonEnvelope childrenD_169 b hb)
def required_170 : Finset Cell := ⟨(([(-4, -1), (-3, 0), (-2, 0), (-2, 1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_170 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-3, 0), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_170 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) required_4), (placedSet 2 (1, 0) required_127)]
def childrenD_170 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) envelope_4), (placedSet 2 (1, 0) envelope_127)]
theorem common_sub_170 : commonEnvelope childrenD_170 ⊆ insert (0, 0) required_170 := by decide
theorem child_required_sub_170 : ∀ j, childrenC_170 j ⊆ insert (0, 0) required_170 := by decide
theorem child_envelope_sub_170 : ∀ j, childrenD_170 j ⊆ envelope_170 := by decide
theorem pivot_mem_170 : (0, 0) ∈ envelope_170 := by decide
theorem children_work_170 : ∀ j, Template HasSnaky 5 (childrenC_170 j) (childrenD_170 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_127 2 (1, 0)).mono (by decide)
theorem row_works_170 : Template HasSnaky 6 required_170 envelope_170 := by
refine compose HasSnaky 5 childrenC_170 childrenD_170 children_work_170 (0, 0)
required_170 envelope_170 pivot_mem_170 child_required_sub_170 child_envelope_sub_170 ?_
intro b hb; exact common_sub_170 (mem_commonEnvelope childrenD_170 b hb)
def required_171 : Finset Cell := ⟨(([(-3, -2), (-3, -1), (-3, 0), (-3, 1), (-2, -1), (-1, -1), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_171 : Finset Cell := ⟨(([(-4, 1), (-4, 2), (-3, -2), (-3, -1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_171 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_6), (placedSet 0 (-4, 1) required_91)]
def childrenD_171 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_6), (placedSet 0 (-4, 1) envelope_91)]
theorem common_sub_171 : commonEnvelope childrenD_171 ⊆ insert (0, 0) required_171 := by decide
theorem child_required_sub_171 : ∀ j, childrenC_171 j ⊆ insert (0, 0) required_171 := by decide
theorem child_envelope_sub_171 : ∀ j, childrenD_171 j ⊆ envelope_171 := by decide
theorem pivot_mem_171 : (0, 0) ∈ envelope_171 := by decide
theorem children_work_171 : ∀ j, Template HasSnaky 5 (childrenC_171 j) (childrenD_171 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_91 0 (-4, 1)).mono (by decide)
theorem row_works_171 : Template HasSnaky 6 required_171 envelope_171 := by
refine compose HasSnaky 5 childrenC_171 childrenD_171 children_work_171 (0, 0)
required_171 envelope_171 pivot_mem_171 child_required_sub_171 child_envelope_sub_171 ?_
intro b hb; exact common_sub_171 (mem_commonEnvelope childrenD_171 b hb)
end SnakyConditional
end OAI
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